If a 0, b 0, c 0,then both the roots of | vedclass

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

Question

(B) The roots of the quadratic equation $ax^2 + bx + c = 0$ are given by the quadratic formula:$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$Case $(i)$: If

Vedclass · Accepted Answer

Have negative real parts

Vedclass · Answer

(B) The roots of the quadratic equation $ax^2 + bx + c = 0$ are given by the quadratic formula:$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$Case $(i)$: If the discriminant $D = b^2 - 4ac \ge 0$,the roots are real.Since $a, b, c > 0$,we have $\sqrt{b^2 - 4ac}  0$,both roots are negative.Case $(ii)$: If $D = b^2 - 4ac $x = \frac{-b}{2a} \pm i \frac{\sqrt{4ac - b^2}}{2a}$Here,the real part is $-\frac{b}{2a}$. Since $a > 0$ and $b > 0$,the real part $-\frac{b}{2a}$ is negative.In both cases,the roots have negative real parts.

If $a > 0, b > 0, c > 0$,then both the roots of the equation $ax^2 + bx + c = 0$:

Similar Questions

In the equation ${x^3} + 3Hx + G = 0$,if $G$ and $H$ are real and ${G^2} + 4{H^3} > 0$,then the roots are

Let $p, q \in Q$. If $2 - \sqrt{3}$ is a root of the quadratic equation $x^2 + px + q = 0$,then:

Find the roots of the equation $\sqrt{3y+1} = \sqrt{y-1}$.

The value of $m$ for which the equation $\frac{a}{x + a + m} + \frac{b}{x + b + m} = 1$ has roots equal in magnitude but opposite in sign is

Find two consecutive positive odd integers whose squares have the sum $290.$

Vedclass Test Series

Exam Paper Generator

Online Exam Module