Question

if alpha , beta are roots of ax^2+bx+c=0 then 1/alpha^2 + 1/beta^2=

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Answer 1

➸ Given:-

• $\bold{\alpha\;\&\;\beta}$ are Roots of the Quadratic Equation ax²+bx+c = 0.

☣ To Find:-

• $\Large{\bold{\frac{1}{{\alpha}^{2}}+\frac{1}{{\beta}^{2}}}}$

❃ Required Response:-

Quadratic Equation → $\sf{ax²+bx+c = 0}$

ᬊ Sum of Roots = $\alpha+\beta = \bf{\frac{-b}{a}}$

ᬊ Product of Roots = $\alpha\beta = \bf{\frac{c}{a}}$

$→\;\Large\bold{\frac{1}{{\alpha}^{2}}+\frac{1}{{\beta}^{2}}}$

$→\;\Large\bold{\frac{\alpha^{2}+\beta^{2}}{(\alpha\beta)^{2}}}$

$→\;\Large\bold{\frac{(\alpha+\beta)^{2}-2\alpha\beta}{(\alpha\beta)^{2}}}$

$→\;\Large\bold{\frac{(\frac{-b}{a})²-2\frac{c}{a}}{(\frac{c}{a})²}}$

$→\;\Large\bold{\frac{\frac{b²}{a²}-\frac{2c}{a}}{\frac{c²}{a²}}}$

$→\;\Large{\red{\bold{\frac{b²-2ac}{c²}}}}$

$\boxed{\tt{@MrMonarque}}$

Hope It Helps You ✌️