Quadratic Equations Questions & Answers: 10th (SSC) Mathematics Part 1 (Algebra), Maharashtra Board

Maharashtra SSC Algebra (Mathematics Part I) Board Paper June 2026

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Q.1 (A)(ii) One of the roots of equation \(x^2 + mx - 5 = 0\) is 2, find the value of \(m\).

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Q.2 (B)(ii) Form the quadratic equation whose roots are 3 and –10.

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Q.2 (B)(iv) Solve the following quadratic equation by factorisation method : \(25m^2 = 9\)

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Q.3 (B)(ii) Solve the following quadratic equation by formula method : \(x^2 - 3x - 2 = 0\)

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Q.4 (ii) The sum of the squares of five consecutive natural numbers is 1455. Find the numbers.

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Q.1 (A)(ii) Out of the following equations which one is not a quadratic equation ?

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Q.1 (B)(iv) Write the following quadratic equation in the form \(ax^2 + bx + c = 0\) :
\[ 2y = 10 - y^2 \]

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Q.2 (B)(iii) Solve the following quadratic equation by factorisation method :
\[ x^2 + x - 20 = 0 \]

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Q.3 (A)(ii) One of the roots of the quadratic equation \(5m^2 + 2m + k = 0\) is \(\dfrac{-7}{5}\). Complete the following activity to find the value of ‘\(k\)’.
Solution :
\(\dfrac{-7}{5}\) is a root of quadratic equation \(5m^2 + 2m + k = 0\).
\(\therefore\) put \(m = \dfrac{-7}{5}\) in the equation.
\(\therefore 5 \times \left(\text{____}\right)^2 + 2 \times \left(\text{____}\right) + k = 0\)
____ \(+\) ____ \(+ k = 0\)
____ \(+ k = 0\)
\(\therefore k =\) ____

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Q.4 (i) The sum of two roots of a quadratic equation is 7 and sum of their cubes is 91, find the equation.

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Q.1 (A)(ii) From the following equations which one is the quadratic equation ?

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Q.2 (A)(ii) Complete the following activity to form a quadratic equation.
Activity :
I am a quadratic equation. → My standard form is ____ . → My roots are 5 and 12. → Sum of my roots ____ . → Product of my roots ____ . → My quadratic equation is ____ .

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Q.2 (B)(ii) Solve the following quadratic equation by factorisation method : \(m^2 + 14m + 13 = 0\)

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Q.3 (B)(ii) Solve the following quadratic equation by using formula method : \(x^2 - 2x - 3 = 0\)

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Q.4 (i) Find the value of ‘m’ if the quadratic equation \((m - 12)x^2 + 2(m - 12)x + 2 = 0\) has real and equal roots.

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Q.1 (A)(ii) Out of the following equations which one is not a quadratic equation ?

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Q.1 (B)(ii) Write the following quadratic equation in standard form : \(2y = 10 - y^2\)

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Q.2 (A)(i) Complete the following activity to solve the quadratic equation \(x^2 + 8x - 48 = 0\) by completing square method.
Activity :
\(\therefore\ x^2 + 8x - 48 = 0\)
\(\therefore\ x^2 + 8x + 16 -\) ____ \(- 48 = 0\)
\(\therefore\ (x + 4)^2 -\) ____ \(= 0\)
\(\therefore\ (x + 4)^2 = 64\)
\(\therefore\ x + 4 =\) ____ or \(x + 4 = -8\)
\(\therefore\ x = 4\) or \(x =\) ____

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Q.2 (B)(ii) Solve the following quadratic equation by factorisation method : \(x^2 - 15x + 54 = 0\)

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Q.3 (B)(iii) Product of Shraddha’s age 2 years ago and 3 years hence is 84. Find her present age.

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Q.5 (i) Three conditions are given below. Write the quadratic equation for each of them satisfy that condition :
(a) If discriminant \(\Delta = 0\)
(b) If discriminant \(\Delta > 0\)
(c) If discriminant \(\Delta < 0\)

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Q.1 (A)(ii) Which equation from the following is quadratic equation ?

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Q.2 (A)(ii) Determine the nature of roots of the following quadratic equation.
Activity :
\(m^2 + 2m + 9 = 0\)
\(a = \) ____ , \(b = 2\), \(c = 9\)
\(b^2 - 4ac = 2^2 - 4 \times 1 \times \) ____
\(= \) ____ \(- 36\)
\(\therefore b^2 - 4ac = \) ____
\(\therefore b^2 - 4ac < 0\)
\(\therefore\) Roots of quadratic equation are not real.

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Q.2 (B)(ii) Find ‘\(k\)’ if \(x = 3\) is a root of quadratic equation \(kx^2 - 10x + 3 = 0\).

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Q.3 (B)(ii) Solve the following quadratic equation by formula method : \(y^2 + \dfrac{1}{3}y = 2\)

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Q.4 (i) Manisha wants to distribute 540 bananas among some students. If 30 students were more, each would get 3 bananas less. Find the number of students.

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Q.1 (A)(i) If 3 is one of the root of the quadratic equation \(kx^2 - 7x + 12 = 0\), then \(k\) = .......................

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Q.2 (A)(ii) If 2 and 5 are the roots of the quadratic equation, then complete the following activity to form quadratic equation :
Activity :
Let \(\alpha = 2\) and \(\beta = 5\) are the roots of the quadratic equation.
Then quadratic equation is :
\(x^2 - (\alpha + \beta)x + \alpha\beta = 0\)
\(\therefore x^2 - (2 +\) ____\()x +\) ____ \(\times 5 = 0\)
\(\therefore x^2 -\) ____ \(x +\) ____ \(= 0\)

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Q.2 (B)(ii) Solve the following quadratic equation using factorisation method :
\(x^2 + x - 20 = 0\)

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Q.3 (B)(i) Solve the following quadratic equation by formula method :
\(3m^2 - m - 10 = 0\)

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Q.4 (i) A tank can be filled up by two taps in 6 hours. The smaller tap alone takes 5 hours more than the bigger tap alone. Find the time required by each tap to fill the tank separately.

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