Question

if a and b are zeroes of the quadratic polynomial 2x2 + 3x - 6, then find the values of (i) a− b

Answer 1

$\huge\text{\underline{Answer}}$

$\sf{\underline{Given }}$

a and b are the zeroes of the given quadratic polynomial.

By using relationship between the zeroes and the coefficient of quadratic polynomial.

$\boxed{\sf{ \alpha + \beta = \frac{ - b}{a} }}$

$\boxed{\sf{ \alpha \beta = \frac{c}{a} }}$

Where alpha and betta are zeroes of polynomial.

$\implies$ $\bold{a + b = \frac{ - 3}{2} }$

$\implies$ $\bold{ ab = \frac{ - 6}{2} }$

$\implies$ $\bold{ab = -3}$

Now using the suitable identity,

$\boxed{\sf{{(a - b)}^{2} = {(a + b)}^{2} - 4ab}}$

$\implies$ $\bold{ {(a - b)}^{2} = { (\frac{-3}{2} )}^{2} - 4 \times - 3}$

$\implies$ $\bold{{(a - b)}^{2} = \frac{9}{4} + \frac{12}{1} }$

$\implies$ $\bold{ {(a - b)}^{2} = \frac{57}{4} }$

$\implies$ $\bold{ (a - b) = \frac{ \sqrt{57} }{2}}$