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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 \(\Delta < 0\)

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 \(\Delta < 0\)

1 answer

Best answer

Answer: (a) \(x^2 - 6x + 9 = 0\) (b) \(x^2 - 5x + 6 = 0\) (c) \(x^2 + x + 1 = 0\)

(a) For \(\Delta = 0\) the roots are real and equal. Take \((x - 3)^2 = 0\), i.e. \(x^2 - 6x + 9 = 0\); here \(\Delta = 36 - 36 = 0\).

(b) For \(\Delta > 0\) the roots are real and unequal. Take \(x^2 - 5x + 6 = 0\); here \(\Delta = 25 - 24 = 1 > 0\).

(c) For \(\Delta < 0\) the roots are not real. Take \(x^2 + x + 1 = 0\); here \(\Delta = 1 - 4 = -3 < 0\).

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report
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