Question

Find the zeroes of the polynomial p(x) = x2 - 4x + 3 and verify the relationship between zeros
coefficients​

Answer 1

Answer:

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Step-by-step explanation:

The given quadratic polynomial is,

p(x) =4x² - 4x - 3

=> 4x² - 6x + 2x - 3

=> 2x( 2x -3) + 1(2x + 3)

=> (2x + 1) (2x -3)

p(x) = 0

(2x + 1) = 0 or (2x-3) = 0

x=-1/2 or x= 3/2

Hence, -1/2 and 3/2 are the zeroes of p(x).

Sum of zeroes = -1/2 + 3/2 = 2/2 = 1 = Coefficient of x / Coefficient of x²

Product of zeroes = (-1/2)(3/2) = -3/4 = Constant term/ Coefficient of x²

Hope this would help you!!

Answer 2

Step-by-step explanation:

${x}^{2} - 4x + 3 = 0 \\ \\ {x}^{2} - x - 3x + 3 = 0 \\ \\ x(x - 3) - 1(x - 3) = 0 \\ \\ (x - 3) \: (x - 1) = 0 \\ \\ x = 3 \: \: \: \: \: or \: \: \: \: x = 1$

Now,

$sum \: of \: roots ( \alpha + \beta ) = 3 + 1 \\ \\ = 4 \: = \frac{ - ( - 4)}{1} = \frac{ - b}{a} \\ \\ product \: of \: roots( \alpha \beta ) = 3 \times 1 \\ \\ = 3 \: = \frac{3}{1} = \frac{c}{a}$

Hope it helps. If you satisfied please mark it brainliest.