If the roots of the equation ax2 + bx + c = 0 are equal in magnitude b

1.	If the roots of the equation ax2 + bx + c = 0 are equal in magnitude but opposite in sign, then which one of the following is correct ?(a) a = 0 (b) b = 0 (c) c = 0 (d) b = 0, c ≠ 0, a ≠ 0.
Answer» (d) b = 0. but a ≠ 0, c ≠ 0. Given equation is ax² + bx + c = 0. ∴Roots are x = \(\frac{-b±\sqrt{b^2-4ac}}{2a}\) Given \(\bigg[\frac{-b+\sqrt{b^2-4ac}}{2a}\bigg]\) = - \(\bigg[\frac{-b-\sqrt{b^2-4ac}}{2a}\bigg]\) ⇒ – b + \(\sqrt{b^2-4ac}\) = b + \(\sqrt{b^2-4ac}\) ⇒ 2b = 0 ⇒ b = 0. but a ≠ 0, c ≠ 0.

If the roots of the equation ax2 + bx + c = 0 are equal in magnitude but opposite in sign, then which one of the following is correct ?(a) a = 0 (b) b = 0 (c) c = 0 (d) b = 0, c ≠ 0, a ≠ 0.

Answer»

(d) b = 0. but a ≠ 0, c ≠ 0.

Given equation is ax² + bx + c = 0.

∴Roots are x = \(\frac{-b±\sqrt{b^2-4ac}}{2a}\)

Given \(\bigg[\frac{-b+\sqrt{b^2-4ac}}{2a}\bigg]\) = - \(\bigg[\frac{-b-\sqrt{b^2-4ac}}{2a}\bigg]\)

⇒ – b + \(\sqrt{b^2-4ac}\) = b + \(\sqrt{b^2-4ac}\)

⇒ 2b = 0 ⇒ b = 0. but a ≠ 0, c ≠ 0.