Question

the zeros ofp (x)=x2-4x+3 are
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Answer 1

Solution:-

Method :- 1

Factorization method

$\rm : \implies {x}^{2} - 4x + 3 = 0$

Splitting into middle term

$\rm : \implies {x}^{2} - 3x - x + 3 = 0$

$\rm : \implies x(x - 3) - (x - 3) = 0$

$\rm : \implies (x - 3)(x - 1) = 0$

$\rm : \implies x = 3 \: \: and \: \: x \: = 1$

Method :- 2

Quadratic formula method

$\boxed{ \rm \: x = \dfrac{ - b \pm \sqrt{D} }{2a} }$

given equation :-

$\rm : \implies {x}^{2} - 4x + 3$

Now compare with

$\rm : \implies {a}^{2} + bx + c = 0$

So

$\rm : \implies a = 1 \: \: b \: = - 4 \: and \: c \: = 3$

Find the Discriminant

$\rm : \implies D = {b }^{2} - 4ac$

Now we get

$\rm : \implies D = ( - 4) {}^{2} - 4 \times 3 \times 1$

$\rm : \implies D = 16 - 12$

$\rm : \implies D = 4$

Now use quadratic formula

$\boxed{ \rm \: x = \dfrac{ - b \pm \sqrt{D} }{2a} }$

$\rm : \implies x = \dfrac{ - ( - 4) \pm \sqrt{4} }{2 \times 1}$

$\rm : \implies x = \dfrac{4 \pm2}{2}$

$\rm : \implies x = \dfrac{4 + 2}{2} \: and \: x = \dfrac{4 - 2}{2}$

$\rm : \implies x = 3 \: \: \: and \: \: x = 1$

Answer 2

Step-by-step explanation:

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