Question

if p(x) =x2 + 2√3x +1 then find the value​

Answer 1

★ Answer :

We have to find the possible value of x.

So, We will factorise the polynomial.

We know that,

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

____________[Put Values]

$\tt{\implies x = \frac{-2\sqrt{3} \pm \sqrt{ 2(\sqrt{3})^2 - 4(1)(1)}}{2(1)} } \\ \\ \tt{\implies x = \frac{-2 \sqrt{3} \pm \sqrt{12 - 4}}{2}} \\ \\ \tt{\implies x = \frac{-2 \sqrt{3} \pm \sqrt{8}}{2}} \\ \\ \tt{\implies x = \frac{-2 \sqrt{3} \pm 2\sqrt{2}}{2}}$

Taking Positive

$\tt{\implies x = \frac{-2 \sqrt{3} + 2\sqrt{2}}{2}} \\ \\ \tt{\implies x = \frac{2(- \sqrt{3} + \sqrt{2}}{2}} \\ \\ \tt{\implies x = - \sqrt{3} + \sqrt{2}}$

Taking Negative

$\tt{\implies x = \frac{-2 \sqrt{3} - 2\sqrt{2}}{2}} \\ \\ \tt{\implies x = \frac{2(- \sqrt{3} + \sqrt{2}}{2}} \\ \\ \tt{\implies x = - (\sqrt{3} + \sqrt{2})}$

Answer 2

p(x)=x²-2√2x+1.

p(2√2)=(2√2)²-(2√2*2√2)+1

p(2√2)=(2√2)²- (2√2)²+1

=0+1.

=1.

Therefore, the answer is 1.