Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficient.x square–5x​

Answer 1

Step-by-step explanation:

Given :-

x²-5x

To find :-

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients ?

Solution :-

Finding zeroes :-

Given Quadratic Polynomial is x²-5x

Let P(x) = x²-5x

=> P(x) = x(x-5)

To get zeroes we write P(x) = 0

=> x(x-5) = 0

=> x = 0 or x-5 = 0

=> x = 0 or x = 5

Zeroes are 0 and 5

Relationship between the zeroes and the coefficients:-

The zeroes are 0 and 5

Let α = 0 and β = 5

On Comparing P(x) with the standard quadratic Polynomial ax²+bx+c

We have

a = 1

b = -5

c = 0

i) Sum of the zeroes = α+β

=> α+β

= 0+(-5)

= -5

= -5/1

= - ( Coefficient of x )/Coefficient of x²

= -b/a

α+ β = -b/a

ii) Product of the zeroes = αβ

=> 0/1

= 0

= Constant term/ Coefficient of x²

= c/a

αβ = c/a

we get

Sum of the zeroes = -b/a

Product of the zeroes = c/a

Verified the relationship between the zeroes and the coefficients of P(x).

Answer:-

The zeroes are 0 and -5

Used formulae:-

• The standard quadratic Polynomial ax²+bx+c

• Sum of the zeroes = -b/a

• Product of the zeroes = c/a