Question

one root of the equation 2x^2-8x-m=0 is 5/2.find the other root and value of m​

Answer 1

Answer:

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Answer 2

The value of m is $\frac{-15}{2}$.

The other root is $\frac{3}{2}$ .

Step-by-step explanation:

Consider the provided information.

$2x^2-8x-m=0$

It is given that 5/2  is the root of the equation.

Substitute x = 5/2 in above equation and solve for m.

$2\left(\frac{5}{2}\right)^{2}-(8)\left(\frac{5}{2}\right)-m=0$

$\left(\frac{25}{2}\right)-(4)(5)-m=0$

$\left(\frac{25}{2}\right)-(20)-m=0$

$\left(\frac{25}{2}\right)-(20)=m$

$m=\left(\frac{25-40}{2}\right)$

$m=\frac{-15}{2}$

Hence, the value of m is $\frac{-15}{2}$

now putting value of m in the provided equation.

$2x^2- 8x-(-\frac{15}{2})=0$

$2x^2- 8x+\frac{15}{2}=0$

Multiply both sides by 2, we get,

$4x^2- 16x+15=0$

$4x^2- 6x-10x+15=0$

$2x(2x-3)-5(2x-3)=0$

$(2x-3)(2x-5)=0$

$x=\frac{3}{2}\ or\ x=\frac{5}{2}$

Therefore, its two roots are $\frac{3}{2}$ and $\frac{5}{2}$.

#Learn more

The zero's of qudartatic polynomial x2 +3x -10=0

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