Question

find the quadratic formula if the zeroes are 3 and -1/2​

Answer 1

Answer:

Let the zeroes of the quadratic polynomial be α=3,β=−3 Then

a+β=3+(−3)=0

αβ=3×(−3)=−9

Sum of zeroes =a+β=0

Product of zeroes =αβ=−9

Then, the quadratic polynomial =x²

−( sum of zeroes )x+ product of zeroes =x²−(0)x+(−9)

=x² −9

Answer 2

Question:-

Find the quadratic equations if the zeroes are 3 and -1/2

Solution :-

Formula to find quadratic equation is

${x}^{2} - x( \alpha + \beta ) + \alpha \beta$

Here,

$\alpha = 3 \: \: and \: \: \beta = - \frac{1}{2}$

are zeroes of the equation

Quadratic equation is

${x}^{2} + x(3 + ( - \frac{1}{2} )) + 3 \times - \frac{1}{2}$

${x}^{2} - x( \frac{5}{2} ) + ( - \frac{3}{2} )$

${x}^{2} - \frac{5}{2}x - \frac{3}{2}$

Multiply the whole equation with 2

$2( {x}^{2} - \frac{5}{2} x - \frac{3}{2} )$

$2 {x}^{2} - 5x - 3$

It is the required quadratic equation