Question

It is given the quadratic equation (q + 1 )x² - 8x + p = 0,where p and q are constants,has two equal real roots.Express p in terms of q.
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Answer 1

Answer:

p = $\frac{16}{q+1}$

Step-by-step explanation:

Since there are 2 equal roots then the value of the discriminant is zero, that is

b² - 4ac = 0

Given

(q + 1)x² - 8x + p = 0 ← in standard form

with a = q + 1, b = - 8, c = p , then

(- 8)² - 4p(q + 1) = 0

64 - 4p(q + 1) = 0 ( subtract 64 from both sides )

- 4p(q + 1) = - 64 ( divide both sides by - 4 )

p(q + 1) = 16 ( divide both sides by q + 1 )

p = $\frac{16}{q+1}$

Answer 2

The curve has two equal roots meaning it’s a tangent that meets the curve at only one point. Therefore, the determinant will be equal to 0.

a = (q + 1)
b = -8
c = p