Question

p(x)=x
${ \times }^{2} - 4x + 3$
​

Answer 1

Answer :

x = 1 , 3

Step-by-step explanation :

Given polynomial,

p(x) = x² - 4x + 3

=> It is of the form ax² + bx + c

      a = 1, b = -4, c = 3

[ a - coefficient of x²

 b - coefficient of x

 c - constant term ]

By sum-product pattern,

>> Find the product of quadratic term [ax²] and constant term [c]

 = x² × 3

 = 3x²

>> find the factors of "3x²" in pairs

 => (x) (3x)

 => (-x) (-3x)

>> From the above, find the pair that adds to get linear term [bx]

     - x - 3x = -4x

>> Split -4x as -x and -3x

      x² - 4x + 3 = 0

     x² - x - 3x + 3 = 0

>> Find the common factor,

    x(x - 1) - 3(x - 1) = 0

     (x - 1) (x - 3) = 0

=> x - 1 = 0 ; x = +1

=> x - 3 = 0 ; x = +3

The zeroes of the given polynomial are 1 and 3.