Question

p(x)=xsquare-4x+3 find the zeros of the quadratic polynomial given below​

Answer 1

EXPLANATION.

Quadratic equation.

⇒ x² - 4x + 3.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ x² - 3x - x + 3 = 0.

⇒ x(x - 3) - 1(x - 3) = 0.

⇒ (x - 1)(x - 3) = 0.

⇒ x = 1  and  x = 3.

                                                                                                                         

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and unequal, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.

Answer 2

Answer:-

• Zeros are 3 and 1

Given:-

$\sf{p(x) = {x}^{2} } - 4x + 3$

To Find:-

• The zeros of the quadratic polynomial

Solution:-

$\sf \Rightarrow \: {x}^{2} { - 4x + 3 = 0}$

$\sf \Rightarrow { {x}^{2} - 3x - x + 3 = 0 }$

$\sf \Rightarrow{( {x}^{2} - 3x) + ( - x + 3) = 0 }$

$\sf \Rightarrow{x(x - 3) - 1(x - 3) = 0}$

$\sf \Rightarrow{(x - 3)(x - 1) = 0}$

$\sf{(x - 3) = 0 }$

$\sf{ \red{x = 3}}$

$\sf{(x - 1) = 0}$

$\sf{ \red{x = 1}}$