If alpha and beta are the roots of the equati | vedclass

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

Question

(D) Given that $\alpha$ and $\beta$ are the roots of the quadratic equation $a x^{2}+b x+c=0$.According to the relationship between roots and coeffici

Vedclass · Accepted Answer

$\frac{b^{2}-2 a c}{a^{2}}$

Vedclass · Answer

(D) Given that $\alpha$ and $\beta$ are the roots of the quadratic equation $a x^{2}+b x+c=0$.According to the relationship between roots and coefficients:Sum of roots: $\alpha+\beta = -\frac{b}{a}$Product of roots: $\alpha \beta = \frac{c}{a}$We know the algebraic identity: $\alpha^{2}+\beta^{2} = (\alpha+\beta)^{2} - 2 \alpha \beta$Substituting the values:$\alpha^{2}+\beta^{2} = \left(-\frac{b}{a}\right)^{2} - 2\left(\frac{c}{a}\right)$$= \frac{b^{2}}{a^{2}} - \frac{2c}{a}$$= \frac{b^{2} - 2ac}{a^{2}}$

If $\alpha$ and $\beta$ are the roots of the equation $a x^{2}+b x+c=0$,find the value of $\alpha^{2}+\beta^{2}$.

Similar Questions

If $\alpha$ and $\beta$ are the roots of the equation ${x^2} - a(x + 1) - b = 0$,then $(\alpha + 1)(\beta + 1) = $

$\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}$ is equal to

Let $[t]$ denote the greatest integer $\leq t$. Then the equation in $x$,$[x]^{2} + 2[x + 2] - 7 = 0$,has

If $p$ and $q$ are the roots of $x^2 + px + q = 0$,then

The exact set of values of $a$ for which the equation ${x^3}(x + 1) = 2(x + a)(x + 2a)$ has four real solutions is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module