If the sum of the roots of the equation ax^2 | vedclass

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

Question

(B) Let the roots of the quadratic equation $ax^2 + bx + c = 0$ be $\alpha$ and $\beta$.From the properties of quadratic equations,we have:Sum of root

Vedclass · Accepted Answer

$2ac = b(a + b)$

Vedclass · Answer

(B) Let the roots of the quadratic equation $ax^2 + bx + c = 0$ be $\alpha$ and $\beta$.From the properties of quadratic equations,we have:Sum of roots: $\alpha + \beta = -\frac{b}{a}$Product of roots: $\alpha \beta = \frac{c}{a}$According to the problem,the sum of the roots is equal to the sum of the squares of the roots:$\alpha + \beta = \alpha^2 + \beta^2$We know that $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha \beta$.Substituting the values:$-\frac{b}{a} = (-\frac{b}{a})^2 - 2(\frac{c}{a})$$-\frac{b}{a} = \frac{b^2}{a^2} - \frac{2c}{a}$Multiply the entire equation by $a^2$:$-ab = b^2 - 2ac$Rearranging the terms:$2ac = b^2 + ab$$2ac = b(a + b)$

If the sum of the roots of the equation $ax^2 + bx + c = 0$ is equal to the sum of the squares of their roots,then:

Similar Questions

If the roots of the equation $12x^2 - mx + 5 = 0$ are in the ratio $2 : 3$,then $m =$

Let $\alpha$ and $\beta$ be the roots of the equation $5x^{2} + 6x - 2 = 0$. If $S_{n} = \alpha^{n} + \beta^{n}$ for $n = 1, 2, 3, \dots$,then:

If the difference of the roots of $x^2 - px + 8 = 0$ is $2$,then the value of $p$ is

The condition that the roots of $x^3-b x^2+c x-d=0$ are in geometric progression is

The difference between two roots of the equation $x^3-13x^2+15x+189=0$ is $2$. Then the roots of the equation are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module