Question

Find the root of quadratic equation 2x^2-7x+3=0 by formula method

Answer 1

GIVEN:

★$2x^{2}-7x+3=0$

TO FIND:

★The roots of the Quadratic equation by formula method.

CONCEPT USED:

★We would find it's roots by standard formula,

of the equation in $ax^{2}+bx+c$ form,which is ;

$\large\purple{\boxed{\dfrac{-b±\sqrt{b^{2}-4ac}}{2a}}}$

ANSWER:

Clearly here,

a = 2

b=-7 &

C=3

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On substituting values, we have;

=$\dfrac{-b±\sqrt{b^{2}-4ac}}{2a}$

=$\dfrac{-(-7)±\sqrt{(-7)^{2}-4\times2\times3}}{2\times2}$

=$\dfrac{7±\sqrt{49-24}}{2\times2}$

=$\dfrac{7±\sqrt{25}}{4}$

=$\dfrac{7±5}{4}$

=$\dfrac{7-5}{4}, \dfrac{7+5}{4}$

=$\dfrac{2}{4}, \dfrac{12}{4}$

=$3,\dfrac{1}{2}$

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We could also find it's zeroes by factorisation,

=>$2x^{2}-7x+3=0$

=>$2x^{2}-x-6x+3=0$

=>$x(2x-1) -3(2x-1)=0$

=>$(x-3) (2x-1) =0$

Hence x = $3, \dfrac{1}{2}$

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Hence the zeroes are $3$&$\dfrac{1}{2}$

$\huge\orange{\boxed{Answer:3, \dfrac{1}{2}}}$