Question

By considering the discriminant, find the
value of the constant p such that the
following equation has equal/repeated
solutions.
4x2 + 8x + p = 0​

Answer 1

Answer:

p = 4

Step-by-step explanation:

A quadratic equation has equal/repeated solutions when a discriminant (Δ) is equal 0.

The formula of a discriminant (Δ) of equation

$ax^2+bx+c=0\\\\\Delta=b^2-4ac$

We have the equation

$4x^2+8x+p=0\to a=4;\ b=8;\ c=p$

substitute

$\Delta=8^2-4\cdot4\cdot p=64-16p\\\\\Delta=0\iff64-16p=0$

subtract 64 from both sides

$-16p=-64$

divide both sides by (-16)

$\dfrac{-16p}{-16}=\dfrac{-64}{-16}\\\\p=4$