Question

If the polynomial 2x³+ax²-14x+b had the sum and product of its zeroes are 5\2and as -4.then the values of a and b are :

Answer 1

here is your answer mate

Answer 2

We know that if a cubic polynomial has zeros represented as
$\alpha \beta \gamma$
and standard cubic polynomial is
$e {x}^{3} + f {x}^{2} + gx + h= 0$

than relation between it's zeros and coefficient are
$\alpha + \beta + \gamma = \frac{ - f}{e} \\ \\ \alpha \beta \gamma = \frac{ - h}{e}$
ATQ

$\alpha + \beta + \gamma = \frac{5}{2} = \frac{ - f}{e} \\ \\\frac{5}{2} = \frac{ - a}{2} \\ \\ a = - 5$
and
$\alpha \beta \gamma = \frac{ - h}{e} = - 4 \\ \\ \frac{ - b}{2} = - 4 \\ \\ b = 8$
So,
$a = - 5 \\ \\ b = 8$
Hope it helps you.