Question

7. Find a quadratic polynomial for which the sum of zeroes is -1/4 and the product of zeroes is 1/4​

Answer 1

$\alpha + \beta = \frac{ - 1}{4} \\ \alpha \beta = \frac{1}{4} \\ p(x) = {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ = {x}^{2} - ( \frac{ - 1}{4}) x + \frac{1}{4} \\ {x}^{2} + \frac{x}{4} + \frac{1}{4}$

Answer 2

Step-by-step explanation:

Given:-

the sum of zeroes is -1/4 and the product

of zeroes is 1/4

To find:-

Find a quadratic polynomial for which the

sum of zeroes is -1/4 and the product of

zeroes is 1/4

Solution:-

Given that

Sum of the zeroes = -1/4

Product of the zeroes = 1/4

Let the zeroes be α and β

then we have

α + β = -1/4

αβ = 1/4

we know that

If α and β are the zeores then the quadratic

polynomial is K[x^2-(α+ β)x +αβ]

Now ,

On Substituting the values in the above formula

=>K[x^2-(-1/4)x +(1/4)]

=>K[x^2+(x/4)++1/4)]

=>K[(4x^2+x+1)/4]

If K=4 then

the required pilynomial is 4x^2+x+1

Answer:-

The quadratic polynomial of the given problem is

4x^2+x+1

Used formulae:-

• If α and β are the zeores then the quadratic
• polynomial is K[x^2-(α+ β)x +αβ]