Question

The product of zeroes of polynomial x2 + 7x + 10 is:
(a) – 7 (b) 1 (c) – 10
(d) 10​

Answer 1

$\huge{\mathfrak{\blue{\underline{Answer}}}}$

The product of the zeroes is equal to

$\large{\mathcal{\green{C/a}}}$

Where

C=10 , a=1

we get

$\huge{\mathfrak{\blue{\underline{C/a=10/1=10}}}}$

option(d) ✔

Answer 2

Question :-

The product of Zeros of polynomial

x² + 7x + 10 is -

Answer :-

→ Product of zeros is 10

→ Sum of zeros is -7

Solution :-

Method (1)

Given equation of polynomial is

$\implies \: \sf{ {x}^{2} + 7x + 10} \: = 0 \\ \\ \implies \: \sf{{x}^{2} + 5x + 2x + 10 = 0} \\ \\ \implies \: \sf{ x(x + 5) + 2(x + 5) = 0} \\ \\ \implies \: \sf{(x + 5)(x + 2) = 0}$

• Case (1) if

→ x + 5 = 0

→ x = -5

• Case (2) if

→ x + 2 = 0

→ x = -2

Zeros of this polynomial are -5 and -2

Therefore ,

• Product of zeros = -5 × (-2) = 10

• Sum of zeros = -5+ (-2) = -7

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Method (2)

We will use direct formula of sum of zeros and product of Zeros.

Given polynomial is

→ x² + 7x + 10 = 0

° Coefficient of x² is 1

° coefficient of x is 7

° constant term is 10 ,

Now ,we know that ,

$\star \sf{product \: of \: zeros \: = \frac{constant}{coefficient \: of \: {x}^{2} } } \\ \\ \implies \: \frac{10}{1} = 10 \\ \\ \rightarrow \boxed{\sf{product \: of \: zeros \: = 10}} \\ \\ \star \sf{ sum \: of \: zeros \: = \frac{ - coefficient \: of \: x}{coefficient \: of \: {x}^{2} }} \\ \\ \implies \: \frac{ - 7}{1} = - 7 \\ \\ \rightarrow \boxed{\sf{sum \: of \: zeros \: = - 7}}$

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