Question

If the zeroes of the polynomial x^2 - bx + c in the ratio 2:3 .Prove that 6b^2 = 25c
${ x}^{2} + bx + c$
$prove \: 6b ^{2} = 25c$
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Answer 1

GOOD MORNING

Let it's two zeros be a and b

WE KNOW THAT

a + b = -b And a × b = c

ACCORDING TO THE GIVEN QUESTION

{ 2a : 3a }

2a + 3a = - b

5a = - b

SQUARING ON BOTH SIDES WE HAVE

a² = b²/25 ... Equation ( i )

3a × 2a = c

6a² = c ... Equation ( ii )

FROM I AND II WE HAVE

c/6 = b²/25

25c = 6b²

Answer 2

Step-by-step explanation:

Answer is given above

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