Question

The quadratic equation whose roots are $5+\sqrt{11}$ and $5-\sqrt{11}$ is,

• A. $x^2-10x+14=0$
• B. $x^2+10x+14=0$
• C. $x^2-5x-14=0$
• D. $x^2-5x+14=0$

Answer 1

The correct option is A $x^2-10x+14=0$

The quadratic equation is of the form $x^2-(\alpha +\beta )x+\alpha \beta =0$


$Let\alpha =5+\sqrt{11}and\beta =5-\sqrt{11}$

$\alpha +\beta =5+\sqrt{11}+5-\sqrt{11}$

$\alpha +\beta =10$

$\alpha \beta =(5+\sqrt{11})(5-\sqrt{11})$

$=25-11=14$

$\left[\right(a+b\left)\right(a-b)=a^2-b^2]$

Substituting value of $\alpha +\beta$ and $\alpha \beta$, the required quadratic equation is $x^2-10x+14=0$

$\text{(a) is corrrect}$