Question

write a quadratic polynomial whose zeroes are -3√2,√2
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Answer 1

Step-by-step explanation:

Given -

• Zeroes of polynomial are -3√2 and √2

To Find -

• A quadratic polynomial

As we know that :-

α + β = -b/a

→ -3√2 + √2 = -b/a

→ -2√2/1 = -b/a .... (i)

And

αβ = c/a

→ -3√2 × √2 = c/a

→ -6/1 = c/a .... (ii)

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

a = 1

b = 2√2

c = -6

As we know that :-

For a quadratic polynomial :-

• ax² + bx + c

→ (1)x² + (2√2)x + (-6)

→ x² + 2√2x - 6

Hence,

The quadratic polynomial is x² + 2√2x - 6

Verification :-

• α + β = -b/a

→ -3√2 + √2 = -2√2/1

→ -2√2 = -2√2

And

• αβ = c/a

→ -3√2 × √2 = -6/1

→ -6 = -6

LHS = RHS

Hence,

Verified...

It shows that our answer is absolutely correct.

Answer 2

$x ^{2} + 2 \sqrt{2x} - 6$