Question

If a.B
are zero's of polynomial 3x²-24x+243. Then find a+B.​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

If $\alpha \: \: and \: \: \beta \:$are the zeroes of the quadratic polynomial $a {x}^{2} + bx + c$

Then

$\displaystyle \: \alpha + \beta \: = - \frac{b}{a} \: \: and \: \: \: \alpha \beta \: = \frac{c}{a}$

GIVEN

a, B are the zeros of the polynomial

$3 {x}^{2} - 24x + 243$

TO DETERMINE

The value of a + B

CALCULATION

The given Quadratic polynomial is

$3 {x}^{2} - 24x + 243$

Comparing with

$a {x}^{2} + bx + c$

We get

$a = 3 \: , \: b = - 24 \: , \: c = 243$

Hence

$\sf{Sum \: of \: the \: Zeroes \: } = \displaystyle \: - \frac{b}{a} = - \frac{ - 24}{3} = 8$

$\implies \: a + B = 8$