Question

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

Answer 1

Answer:

Given polynomial is

${x}^{2} - 4x + 3$

Now,

${x }^{2} - 4x + 3 \\ \\ {x}^{2} - 3x - x + 3 \\ \\ x(x - 3) - 1(x - 3) \\ \\ (x - 3)(x - 1)$

So,

zeros of the polynomial are 3,1

RELATIONSHIP:-)

$sum = \frac{ - coeff.of \: x}{ \: \: \: \: coeff.of \: {x}^{2} } \\ \\ 3 + 1 = \frac{ - (4)}{1} \\ \\ 4 = 4 \: \: \: \: \: \:: Hence \:verified$

$product = \frac{const.}{coeff.of \: {x}^{2}} \\ \\ 3 \times 1 = \frac{3}{1} \\ \\ 3 = 3 \: \: \: \: \: \: Hence \:verified$

Answer 2

Answer

3 = 3 relationship between zeroes and

coefficients.

Step-by-step explanation:

Accustomed Question

Find the zeroes of the polynomial p(x) = x2 - 4x + 3

Case (1)

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

Case (2)

Verify the relationship between zeroes and coefficients.

Verification

Before this ( By formula )

Total = coefficient of x / x²

= 3 + 1 = ( - 4 ) / 1

= 4 = 4

= Constant / coefficient of x²

= 3 × 1 = 3 / 1

= 3 = 3

Hence, Proved the relationship between zeroes and coefficients.

$BeBrainly$