Question

Solve this
Two real numbers $\alpha \&\beta$ ared such that $\alpha +\beta =3,\alpha -\beta =4$, then $\alpha \&\beta$ are the roots of the quadratic equation:
(A) 4x² - 12x - 7 = 0 (B) 4x² - 12x + 7 = 0 (C) 4x²- 12x + 25 = 0 (D) none of these

Answer 1

$$\begin{gathered} \alpha +\beta =3\_\_\_\_\_\_\_\_\_\_\_\_\left(1\right) \\ \alpha -\beta =4\_\_\_\_\_\_\_\_\_\_\left(2\right) \\ Addequation1and2 \\ 2\alpha =7 \\ \alpha =\frac{7}{2} \\ \alpha +\beta =3 \\ \frac{7}{2}+\beta =3 \\ \beta =-\frac{1}{2} \\ \alpha \beta =-\frac{7}{4} \\ Quadraticequationwithroots\alpha and\beta isgivenby \\ {x}^2-\left(\alpha +\beta \right)x+\alpha \beta =0 \\ {x}^2-3x-\frac{7}{4}=0 \\ 4x^2-12x-7=0 \end{gathered}$$