Question

Find the quadratic polynomial whose zeroes
are (2/3)and (-1/4)
Verify the relationship between the
coefficients and the zeroes of the
polynomials.​

Answer 1

Explanation:

Given -

• Zeroes are 2/3 and -1/4

To Find -

• A quadratic polynomial

Now,

→ α + β = -b/a

→ 2/3 + (-1/4) = -b/a

→ 2/3 - 1/4 = -b/a

→ 8 - 3/12 = -b/a

→ 5/12 = -b/a ..... (i)

And

→ αβ = c/a

→ 2/3 × -1/4 = c/a

→ -2/12 = c/a ...... (ii)

Now, From (i) and (ii), we get :-

a = 12

b = -5

c = -2

As we know that :-

For a quadratic polynomial :-

• ax² + bx + c

→ (12)x² + (-5)x + (-2)

→ 12x² - 5x - 2

Hence,

The quadratic polynomial is 12x² - 5x - 2

Verification :-

→ α + β = -b/a

→ 2/3 - 1/4 = -(-5)/12

→ 8 - 3/12 = 5/12

→ 5/12 = 5/12

LHS = RHS

And

→ αβ = c/a

→ 2/3 × -1/4 = -2/12

→ -2/12 = -2/12

LHS = RHS

Hence,

Verified...

It shows that our answer is absolutely correct.