Question

Find a quadratic polynomial the sum and product of whose zeroes are -3 and 2 respectively.

Answer 1

Given:-

• Sum of zeros is -3
• Product of zeros is 2

To find :-

• Quadratic polynomial

Solution

As we know that ,

If ${\alpha,\beta}$ are the zeros of Quadratic polynomial then required Quadratic polynomial is

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

So, here

$\alpha + \beta = sum \: \: of \: \: zeros$

$\alpha \beta = product \: of \: zeros$

ATQ ,

$\alpha + \beta = \: - 3$

$\alpha \beta = 2$

Required Quadratic polynomial is

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

$x {}^{2} - ( - 3)x + 2$

$x {}^{2} + 3x + 2$

So, the required polynomial is x² + 3x + 2

Verification:-

Now we got Quadratic polynomial since its sum of zeros must be -3 and product of zeros is 2

Finding zeros to the Quadratic polynomial

x² + 3x + 2

Splitting the middle term

${x^2+ x + 2x + 2}$

$x(x+1) +2(x+1)$

$(x+1)(x+2)$

${x= -1 , -2}$

Sum of zeros = -1-2

Sum of zeros = -3 (Verified)

Product of zeros = (-1)(-2)

Product of zeros = 2(Verified)