Question

solve by quadratic formula 2x²+5√3+6​

Answer 1

Answer:

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Quadratic formula

$\red{\bigstar}\boxed{\sf{x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}}$

when,

ax² + bx + c = 0

where,

a , b , c are constants and a ≠ 0

and x is unknown.

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Now,

comparing 2 x²  + 5√3 + 6 with ax² + bx + c

• a = 2
• b = 5√3
• c = 6

putting values in quadratic formula

$\implies\sf{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}$

$\implies\sf{x=\dfrac{-5\sqrt3 \pm \sqrt{(5\sqrt3)^2 - 4 (2)(6)}}{2(2)}}$

$\implies\sf{x=\dfrac{-5\sqrt3 \pm \sqrt{75 - 48}}{4}}$

$\implies\sf{x=\dfrac{-5\sqrt3 \pm \sqrt{27}}{4}}$

$\implies\sf{x=\dfrac{-5\sqrt3 \pm 3\sqrt{3}}{4}}$

so,

$\longrightarrow\boxed{\sf{x=\dfrac{-5\sqrt3 + 3\sqrt{3}}{4}=\dfrac{-2\sqrt{3}}{4}=\dfrac{-\sqrt{3}}{2}}}$

and

$\longrightarrow\boxed{\sf{x=\dfrac{-5\sqrt3 - 3\sqrt{3}}{4}=\dfrac{-8\sqrt{3}}{4}=-2\sqrt3}}$

are two zeroes of quadratic polynomial 2x² + 5√3 + 6 .