For what values of k will the equation x^2 - | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For a quadratic equation $ax^2 + bx + c = 0$ to have equal roots,the discriminant $D = b^2 - 4ac$ must be equal to $0$.Here,$a = 1$,$b = -2(1 + 3k

Vedclass · Accepted Answer

$2, - \frac{10}{9}$

Vedclass · Answer

(B) For a quadratic equation $ax^2 + bx + c = 0$ to have equal roots,the discriminant $D = b^2 - 4ac$ must be equal to $0$.Here,$a = 1$,$b = -2(1 + 3k)$,and $c = 7(3 + 2k)$.Setting $D = 0$:$[-2(1 + 3k)]^2 - 4(1)(7(3 + 2k)) = 0$$4(1 + 3k)^2 - 28(3 + 2k) = 0$Divide by $4$:$(1 + 3k)^2 - 7(3 + 2k) = 0$$1 + 6k + 9k^2 - 21 - 14k = 0$$9k^2 - 8k - 20 = 0$Factor the quadratic equation:$9k^2 - 18k + 10k - 20 = 0$$9k(k - 2) + 10(k - 2) = 0$$(9k + 10)(k - 2) = 0$Thus,$k = 2$ or $k = -\frac{10}{9}$.

For what values of $k$ will the equation $x^2 - 2(1 + 3k)x + 7(3 + 2k) = 0$ have equal roots?

Similar Questions

Number of integral values of $m$ for which ${x}^2 + 5m{x} - 3m + 1 < 0$ $\forall x \in R$ is (where ${.}$ denotes the fractional part function).

The roots of the equation $ix^2 - 4x - 4i = 0$ are

If $\alpha, \beta, \gamma, \delta$ are the roots of $x^4 - 100x^3 + 2x^2 + 4x + 10 = 0$,then $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} + \frac{1}{\delta}$ is equal to:

If $x+\frac{1}{x}=5,$ then $x^{6}+\frac{1}{x^{6}}$ is

$I. x^{2}+10 x+24=0$
$II. 4 y^{2}-17 y+18=0$

Vedclass Test Series

Exam Paper Generator

Online Exam Module