Question

Find the quadratic polynomial whose zeros are 2 and 6. Verify the
elation between the coefficients and the zeros of the polynomial.​

Answer 1

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Answer 2

Step-by-step explanation:

Given -

• Zeroes are 2 and 6

To Find -

• The quadratic polynomial
• Verify the relationship between the zeroes and the coefficient.

Now,

As we know that :-

• α + β = -b/a

→ 2 + 6 = -b/a

→ 8/1 = -b/a ...... (i)

And

• αβ = c/a

→ 2 × 6 = c/a

→ 12/1 = c/a ..... (ii)

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

a = 1

b = -8

c = 12

As we know that :-

For a quadratic polynomial :-

• ax² + bx + c

→ (1)x² + (-8)x + (12)

→ x² - 8x + 12

Hence,

The quadratic polynomial is x² - 8x + 12

Verification :-

As we know that :-

• α + β = -b/a

→ 2 + 6 = -(-8)/1

→ 8 = 8

LHS = RHS

And

• αβ = c/a

→ 2 × 6 = 12/1

→ 12 = 12

LHS = RHS

Hence,

Verified...