Question

find the zeros of the equation p(x) and verify the relationship between the zeros and the coefficient p(x)=x^2-10x+16​

Answer 1

Step-by-step explanation:

$x {}^{2} - 10x + 16 \\ x {}^{2} - 8x - 2x + 16 \\ x(x - 8) - 2(x - 8) \\ (x - 8)(x - 2) \\ x = 8 = \alpha \\ x = 2 = \beta$

$\alpha + \beta = - b \div a = - 10 \div 1 = - 10$

$\alpha \beta = c \div a = 16 \div 1 = 16$

Answer 2

$\purple {\sf{\underline {Solution:-}}}$

According to the question,

${x}^{2} - 10x + 16 = 0$

$⟹ {x}^{2} - 8x - 2x + 16 = 0$

$⟹ x( x - 8) - 2(x - 8) = 0$

$⟹ (x - 8)(x - 2) = 0$

$⟹x - 8 = 0 \: \: or \: \: x - 2 = 0$

$⟹x = 8 \: \: or \: \: x = 2$

Now,

$p(x) = {x}^{2} - 10x + 16$

$p(8) = {8}^{2} - 10 \times 8 + 16$

$\: \: \: \: \: \: \: \: \: = 64 - 80 + 16$

$\: \: \: \: \: \: \: \: \: = 80 - 80$

$\: \: \: \: \: \: \: \: \: = 0$

And,

$p(x) = {x}^{2} - 10x + 16$

$p(2) = {2}^{2} - 10 \times 2 + 16$

$\: \: \: \: \: \: \: \: \: = 4 - 20 + 16$

$\: \: \: \: \: \: \: \: \: = 20 - 20$

$\: \: \: \: \: \: \: \: \: = 0$

• $\green {\sf {Hence, x = 8 \:\:or\:\: x = 2}}$

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