Question

if the difference between the roots of the equation x2+px+7=0 is 6. find the values of p
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Answer 1

Answer:the values of p is +8 or -8

Answer 2

Given:

• The difference between the roots of the equation x²+px +7 is 6.

To find :

• The value of P

Solution :

• p(x)= x² + px + 7

let the roots be :

$\bold{\alpha \: and \: \beta }$

Here,

a= 1 , b = p and c = 7.

$\star \: \alpha + \beta = \frac{ - b}{a} = \frac{ - p}{1} = - p$

$\star \: \alpha \beta = \frac{c}{a} = \frac{7}{1} = 7$

A/Q

$\implies \: \alpha - \beta = 6 \\ \\ \implies \: \sqrt{ {(( \alpha + \beta )}^{2} - 4 \alpha \beta } = 6 \\ \\ \implies \: \sqrt{ {p}^{2} - 4(7)} = 6 \\ \\ \implies \: {p}^{2} - 28 = 36 \\ \\ \implies \: {p}^{2} = 36 + 28 \\ \\ \implies \: p = \sqrt{64} \\ \\ \implies \: p = 8$

Hence , the value of p is 8.