Question

Find the roots of the quadratic equation 3x2

– 5x + 2 = 0. (By using quadratic formula)​

Answer 1

Answer -

$\longmapsto\boxed{x = 1, \: \frac{2}{3} }$

Solution -

Refer to the Attachment..

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Answer 2

Given:-

p(x)=3x²-5x+2=0

To find:-

the roots of p(x) (by using the quadratic formula)​.

Solution:-

p(x)=3x²-5x+2=0

Here, a = 3, b = -5 and c = 2.

Using the quadratic formula,

$\purple\succ{\underline{\boxed{\bf{x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}}}}$

$\red\implies\sf{x=\frac{-5\pm\sqrt{(-5)^{2} -4(3)(2)} }{2\times3}$

$\red\implies\sf{x=\frac{5\pm\sqrt{25-24} }{6}$

$\red\implies\sf{x=\frac{5\pm\sqrt{1} }{6}$

$\red\implies\sf{x=\frac{5-\sqrt{1} }{6};\frac{5+\sqrt{1} }{6}}$

$\red\implies\sf{x=\frac{5-1}{6};\frac{5+1}{6}}$

$\red\implies\sf{x=\frac{4}{6};\cancel{\frac{6}{6}}}$

$\red\implies\sf{x=\frac{2}{3};1}$

∴ $\tt{\frac{2}{3}}$ and 1 are the roots of the quadratic equation 3x²-5x+2=0.