Question

If a and b are zeroes of the quadratic polynomial 2x²+3x+-6, then find the value of : a²+b²

Answer 1

Answer:-

$\sf{The \ value \ of \ a^{2}+b^{2} \ is \ \frac{33}{4}.}$

Given:

• $\sf{The \ given \ quadratic \ polynomial \ is}$
• $\sf{2x^{2}+3x-6}$

• $\sf{Zeroes \ of \ the \ polynomial \ are \ a \ and \ b.}$

To find:

$\sf{The \ value \ of \ a^{2}+b^{2}}$

Solution:

$\sf{The \ given \ quadratic \ polynomial \ is}$

$\sf{2x^{2}+3x-6}$

$\sf{Here, \ a=2, \ b=3 \ and \ c=-6}$

$\sf{Sum \ of \ zeroes=\frac{-b}{a}}$

$\sf{\therefore{a+b=\frac{-3}{2}...(1)}}$

$\sf{Product \ of \ zeroes=\frac{c}{a}}$

$\sf{\therefore{ab=-3...(2)}}$

$\sf{According \ to \ the \ identity.}$

$\boxed{\sf{a^{2}+b^{2}=(a+b)^{2}-2ab}}$

$\sf{...from \ (1) \ and \ (2)}$

$\sf{a^{2}+b^{2}=(\frac{-3}{2})^{2}-2(-3)}$

$\sf{\therefore{a^{2}+b^{2}=\frac{9}{4}+6}}$

$\sf{\therefore{a^{2}+b^{2}=\frac{9+24}{4}}}$

$\sf{\therefore{a^{2}+b^{2}=\frac{33}{4}}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ a^{2}+b^{2} \ is \ \frac{33}{4}.}}}$