Question

Q9. Write a quadratic polynomial, sum of whose zeroes is 2 and product is - 8.​

Answer 1

Given :-

The Sum of zeroes of quadratic polynomials = 2 and The product of quadratic polynomials = -8

[ • Quadratic polynomial is a polynomial which has highest degree of power is 2 .

• It can be expressed is as ax^2 + bx + c = 0 where a, b and c are real numbers ]

Solution :-

Let's compare quadratic equation with

ax^2 + bx + c .

Let the zeroes of quadratic polynomials be α and β

It is given that the sum and product of zeroes is 2 and -8 .

Therefore ,

α + β = -b / a = 2

α * β = c / a = -8

Therefore,

x^2 + ( α + β )x + αβ

Put the required values in the formula,

x^2 + ( 2)x + -8

x^2 + 2x - 8

Hence, The quadratic equation is x^2 + 2x - 8 $.$

Answer 2

$\huge\fcolorbox{black}{lime}{Answer}$

Given :-

The Sum of zeroes of quadratic polynomials = 2 and The product of quadratic polynomials = -8

[ • Quadratic polynomial is a polynomial which has highest degree of power is 2 .

• It can be expressed is as ax^2 + bx + c = 0 where a, b and c are real numbers ]

Solution :-

Let's compare quadratic equation with

ax^2 + bx + c .

Let the zeroes of quadratic polynomials be α and β

It is given that the sum and product of zeroes is 2 and -8 .

Therefore ,

α + β = -b / a = 2

α * β = c / a = -8

Therefore,

x^2 + ( α + β )x + αβ

Put the required values in the formula,

x^2 + ( 2)x + -8

x^2 + 2x - 8

Hence, The quadratic equation is x^2 + 2x - 8 ..