Question

Find a quadratic polynomial each with the given number as the sum and product of its zeros respectively (i) 1/4,-1

Answer 1

Answer:

SUM OF ZEROES : 1/4

PRODUCT OF ZEROES: -1

Q.P= X²-(SX)+P

Q.P = X²-1/4X -1

MULTIPLYING BY 4

(BECAUSE THE DENOMINATOR IS 4)

OR YOU CAN TAKE THE L.C.M

NOW THE Q.P IS 4X²-X-4

Answer 2

We know,

• Sum of zeroes = α+β

• Product of zeroes = α β

• Sum of zeroes = α+β = 1/4

• Product of zeroes = α β = -1

To Find:

• Find a Quadratic Polynomial?

SolutiOn:

∴ If α and β are zeroes of any quadratic polynomial,

then the quadratic polynomial equation can be written directly as:-

➡ x²–(α+β)x +αβ = 0

➡ x²–(1/4)x +(-1) = 0

➡ 4x²–x-4 = 0

Hence,

4x²–x–4 is the quadratic polynomial.