Question

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Answer 1

Explanation:

Given :-

4x²-x-5

To find:-

Find the zeroes of the quadratic polynomial and verify the relationship between the zeroes and the coefficients ?

Solution:-

Finding zeroes :-

Given quadratic polynomial = 4x²-x-5

Let P(x) = 4x²-x-5

=> 4x²+4x-5x-5

=> 4x(x+1)-5(x+1)

=> (x+1)(4x-5)

P(x) = (x+1)(4x-5)

To get zeroes of P(x) we write P(x) = 0

=> (x+1)(4x-5) = 0

=> x+1 = 0 or 4x-5 = 0

=> x = -1 or 4x = 5

=> x = -1 or x = 5/4

The zeroes are -1 and 5/4

Verifying the relationship between the zeroes and the coefficients:-

Given quadratic polynomial = 4x²-x-5

On Comparing this with the standard quadratic polynomial ax²+bx+c

a = 4

b = -1

c = -5

And Zeroes = -1 and 5/4

Let A = -1 and B = 5/4

Sum of the zeroes = -1+(5/4)

=> (-4+5)/4

=> 1/4

=> -(1)/4

=> -(coefficient of x )/Coefficient of x²

=> -b/a

Therefore, Sum of the zeroes = -b/a

Product of the zeroes =

= (-1)(5/4)

= -5/4

= Constant term/ Coefficient of x²

= c/a

Therefore, product of the zeroes = c/a

Verified the given relations in the given problem

Answer:-

The zeroes of the given Quadratic Polynomial are -1 and 5/4

Used formulae:-

• The standard quadratic polynomial is ax²+bx+c
• Sum of the zeroes = -b/a
• Product of the zeroes = c/a

Answer 2

Explanation:

I have attached the solution.