Question

For which values of p does the following equation has
equal boots ? 2x²-P x + 8 = 0​

Answer 1

Step-by-step explanation:

D = b2-4ac

a=2, b=-p, c=8

p2-4(2)(8)=0

p2=64

p=8

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Answer 2

Given : A quadratic equation 2x² - px + 8 = 0

To Find : Value of x

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As we know that :

If the roots are equal then ,

D (discrminant) = 0

$\: \:$

Formula for finding D (discrminant) :

$\:$

$\underline{\boxed{\sf\purple{\bigstar \: D = {b}^{2} - 4ac}}}$

Here

$\: \:$

• a = 2
• b = p
• c = 8

$\: \:$

Put the values and solve !!

$\:$

$\tt:\implies \: D = {b}^{2} - 4ac \\ \\ \\ \tt:\implies \: {p}^{2} - (4 \times 2 \times 8) = 0 \\ \\ \\ \tt:\implies \: {p}^{2} - 64 = 0 \\ \\ \\ \tt:\implies \: {p}^{2} = 64 \\ \\ \\ \tt:\implies \: p = \sqrt{64} \\ \\ \\ \tt:\implies \: p = \underline{\boxed{\tt\purple{8}}}\bigstar \\ \\ \\ \\ \sf\therefore{\underline{Hence, \: the \: value \: of \: p \: is \: \bold{8}.}}$