Respuesta :
Answer :
The value of q for, the given quadratic equation is 40
Step-by-step explanation :
Given quadratic equation as :
x² - 14 x + q = 0
And , Difference between the roots of equation is 6
Let A , B be the roots of the equation
So, A - B = 6
The roots of the quadratic equation ax² + bx + c = 0 as can be find as :
x = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]
x = [tex]\frac{14\pm \sqrt{(-14)^{2}-4\times 1\times q}}{2\times 1}[/tex]
or, x = [tex]\frac{-14\pm \sqrt{196-4 q}}{2}[/tex]
Or, x = [tex]\frac{-14\pm \sqrt{196-4 q}}{2}[/tex]
So , The roots are
A = [tex]-7 + \frac{\sqrt{196-4q}}{2}[/tex]
And B = [tex]-7 - \frac{\sqrt{196-4q}}{2}[/tex]
∵ The difference between the roots is 6
So, A - B = 6
Or, ( [tex]-7 + \frac{\sqrt{196-4q}}{2}[/tex] ) - ( [tex]-7 - \frac{\sqrt{196-4q}}{2}[/tex] ) = 6
Or, ( - 7 + 7 ) + 2 ( [tex]\sqrt{196-4q}[/tex] = 6
Or, 0 + 2 ( [tex]\sqrt{196-4q}[/tex] = 6
∴ 196 - 4 q = 36
or, 4 q = 196 - 36
or 4 q = 160
∴ q = [tex]\frac{160}{4}[/tex]
I.e q = 40
S0, The value of q = 40
Hence The value of q for, the given quadratic equation is 40 . Answer
