Question

Find the zeroes of the polynomial
$4x^{2} -4x+1$

Answer 1

Given :

Quadratic polynomial

$4 {x}^{2} - 4x + 1$

What to find out = zeroes of polynomial?

Solution :-

Factorise by splitting middle term

$4 {x}^{2} - 4x + 1 = 0 \\ \\ 4 {x}^{2} - 2x - 2x + 1 = 0 \\ \\ 2x(2x - 1) - 1(2x - 1) = 0 \\ \\ (2x - 1)(2x - 1) = 0 \\ \\ (2x - 1) {}^{2} = 0 \\ \\ (2x - 1) = 0 \\ \\ 2x =1 \\ \\ x = ±\frac{1}{2} \: \: \: \: answer$

Extra information :-

• a quadratic polynomial is a polynomial of degree two, also called second-order polynomial. That means the exponents of the polynomial's variables are no larger than 2

Answer 2

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Question}}}}}}}}$

$\sf 4x^2 - 4x + 1$

find the zeros of the polynomial

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Solution}}}}}}}}$

• solve by middle term split

$\sf\implies 4x^2 -4x + 1=0$

$\sf\implies 4x^2 -2x - 2x + 1 = 0$

$\sf\implies 2x(x - 1)-2(x-1)= 0$

$\sf\implies(2x-2)(x-1) = 0$

• zeros in the equation

$\sf\implies 2x- 2 = 0$

$\sf\implies 2x= 2$

$\sf\implies x =\dfrac{1}{2}$

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$\sf\implies x-1 = 0$

$\sf\implies x= 1$

Zeros of the equation are :-

${\bold{\blue{\boxed{\bf{\dfrac{1}{2}}}}}}$ And ${\bold{\blue{\boxed{\bf{1}}}}}$

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