Question

the sum and the product of zeroes of the quadratic polynomial are -1/2 and -3 find the quadratic polynomial

Answer 1

Explanation:

Let a and b be zeros

a+b = -1/2

a = -1/2 - b

ab = -3

(-1/2 -b) b = -3

-b/2 -b^2 +3=0

2b^2 +b - 6 = 0

b = 3/2 or b = -2

If b= 3/2 or a +b = -1/2

a +b = -1/2 or a = -1/2 +2

a = -4/2 or a = -1+4/2

a = -2 or a = 3/2

If (a, b) => (-2, 3/2)

x^2+ 1/2x -3 = 0

2x^2 +x - 6 = 0

Answer 2

$\large \underline{ \underline{ \sf \: Solution : \: \: \: }}$

Given ,

$\star$Sum of zeroes = - 3

$\star$Product of zeroes = -1/2

We know that , Quadratic equation is given by :

$\large \fbox{ \fbox{ \sf {x}^{2} - (sum \: of \: zeroes)x + (product \: of \: zeroes) = 0}}$

$</p><p> \to \sf {(x)}^{2} - ( - \frac{1}{2} )x + ( - 3 ) = 0 \\ \\ \to \sf {(x)}^{2} + (\frac{1}{2}) x- 3 = 0 \\ \\ \to \sf 2{(x)}^{2} + x - 6 = 0$

Hence , 2x² + x - 6 is the required quadratic polynomial