Question

$2x^2-9x+10=0,$ when:

• A. $x\in N$
• B. $x\in Q$
• C. $x$ has complex roots
• D. None

Answer 1

The correct option is A $x\in N$

Consider the given equation.

$2x^2-9x+10=0$

Comparing that,

$a{x}^2+bx+c=0$ we get,

$a=2,b=-9,c=10$

Then, using quadratic equation formula,

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{9\pm \sqrt{{(-9)}^2-4\times 2\times 10}}{2\times 2}$

$x=\frac{9\pm \sqrt{81-80}}{4}$

$x=\frac{9\pm 1}{4}$

Taking +ive,

$x=\frac{9+1}{4}=\frac{10}{4}=\frac{5}{2}$

Taking –ive,

$x=\frac{9-1}{4}=\frac{8}{4}=2$

option $\left(B\right)$ is correct

Hence, this is the answer.