Question

If a and B are the zeros of the quadratic polynomial 2x² + 5x + 2, then find the value of a⁴ + b⁴.
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Answer 1

Step-by-step explanation:

Given :-

2x² + 5x + 2

To Find :-

a⁴+ b⁴.

Solution :-

On spillting middle term

2x² + (4x + x) + 2 = 0

2x² + 4x + x + 2 = 0

2x(x + 2) + 1(x + 2) = 0

(x + 2)(2x + 1) = 0

Either

x + 2 = 0

x = 0 - 2

x = -2

Or,

2x + 1 = 0

2x = 0 - 1

2x = -1

x = -1/2

So,

α⁴ + β⁴

(-2)⁴ + (-1/2)⁴

16 + 1/16

256 + 1/16

257/16

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Answer 2

Answer :

• a⁴ + b⁴ = 257/16

Given that :

• a and b are zeros of 2x² + 5x + 2

Step-by-step explanation:

a is a zero of p(x)

Then, p(a) = 0

→ 2a² + 5a + 2 = 0

→ 2a² + 4a + a +2 = 0

→ 2a(a+2) +(a+2) = 0

→ (2a+1)(a+2) = 0

→ 2a + 1 = 0 , a+2 = 0

→ 2a = -1 , a = -2

→ a = -1/2 , a = -2

b is also a zero of p(b)

Then, p(b) = 0

→ 2b² + 5b + 2 = 0

→ 2b² + 4b + b + 2 = 0

→ 2b(b+2) +(b+2) = 0

→ (2b +1)(b+2) = 0

→ 2b+1 = 0 , b+2 = 0

→ 2b = -1 , b = -2

→ b = -1/2 , b = -2

As a and b are two different zeros of p(x)

Therefore , we put a = -1/2 and b = -2

→ a⁴ + b⁴

→ (-1/2)⁴ + (-2)⁴

→ 1/16 + 16

→ (1 + 256) /16

→ 257/16

If we consider a = -2 and b = -1/2

Then , we also get the same answer according to commutative property of addition,

(a+b) = (b+a)

So, the value of a⁴ + b⁴ = 257/16

I hope it helps you