Question

Find the zeros of the quadratic polynomial x^2-2x-8 and verify the relation between the zeros and its coefficients

Answer 1

Let p and q be the zeroes of the p(x).

Given: p(x) = x^2 - 2x - 8; a=1, b=(-2), c=(-8)

To find: 1)Zeroes of the p(x)

2)Relation between the zeroes and it's coefficients

1)Let, p(x) = 0

Therefore,

=> x^2 - 2x - 8 = 0

=> x^2 - (4 - 2)x - 8 = 0

=> x^2 - 4x + 2x - 8 = 0

=> x(x - 4) + 2(x - 4) = 0

=> (x - 4)(x + 2) = 0

=> x - 4 = 0 or x + 2 = 0

=> x = 4 or x = (-2)

So, p = 4 and q = (-2)

2)Now, p + q = (-b/a)

4 + (-2) = -(-2)/1

2 = 2

LHS = RHS

Also, pq = c/a

4(-2) = (-8)/1

(-8) = (-8)

LHS = RHS

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