Question

Given the equation px^2 + 8x + 8 = 0 has equal roots find the value
of p.

Answer 1

$\\ \sf\longmapsto px^2+8x+8=0$

Equal roots means Discriminate=0

$\\ \sf\longmapsto D=0$

$\\ \sf\longmapsto b^2-4ac=0$

$\\ \sf\longmapsto 8^2-4(8)(p)=0$

$\\ \sf\longmapsto 64-32p=0$

$\\ \sf\longmapsto 32p=64$

$\\ \sf\longmapsto p=2$

Answer 2

Answer:

• p = 2

Step-by-step explanation:

Since the roots are equal, the given equation should be a perfect square:

• px² + 8x + 8 = 0

Let p = 2q, since with odd value of p we can't get a perfect square:

• 2qx² + 8x + 8 = 0, divide all terms by 2
• qx² + 4x + 4 = 0

The value of q should be 1 to make it a perfect square:

• x² + 4x + 4 = 0
• (x + 2)² = 0

Since q = 1, the value of p is:

• p = 2q = 2*1 = 2