Question 64

If the two roots of a quadratic equation are α, β where α + β = 8 and α - β = 2, then the equation is:

Solution

Given that

α + β = 8 .........1 and α - β = 2...........2

by solving both equation and adding the both equation we get

$$α + β+α - β=10$$

$$2α=10$$

$$α=5$$

$$β=3$$

We substitute these values into the expression

$$\displaystyle{x}^{2}-{\left(\alpha+\beta\right)}{x}+\alpha\beta=0$$

$$\displaystyle{x}^{2}-{(5+3)}{x}+5\times3=0$$

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

\displaystyle{x}^{2}-{\left(\alpha+\beta\right)}{x}+\alpha\beta={

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