Question

Find the zeros of the quadratic polynomial x² + 7x + 10, and verify the relationship between the zeros and the coefficients.​

Answer 1

Step-by-step explanation:

Given quadratic polynomial x2 + 7x + 10

Using factorisation (splitting the middle term)

x2 + 7x + 10 = 0

x2 + (5x + 2x) + 10 = 0

x2 + 5x + 2x + 10 = 0

x(x + 5) + 2 (x + 5) = 0

(x + 5) (x + 2) = 0

Hence, zeroes of a given quadratic polynomial are – 5 and – 2.

Sum of zeroes = -2+(-5) = -2-5

= -7/1 = -x coefficient /x² coefficient

Product of zeroes = (-2)(-5)

= 10/1 = constant/x² coefficient

Answer 2

Answer:

Here, a = 1, b = 7,& c = 10.

${x}^{2} + 7x + 10$

${x}^{2} + 2x + 5x + 10$

$x(x + 2) + 5(x + 2)$

$(x + 5)(x + 2)$

Therefore x = -5 or -2 .

$sum \: of \: zeroes \: = \frac{ - b}{a}$

$- 5 + ( - 2) = \frac{ - ( 7)}{1}$

$- 5 - 2 = - 7$

$- 7 = - 7$

$product \: of \: zeroes \: = \frac{c}{a}$

$- 5 \times - 2 = \frac{10}{1}$

$10 = 10$

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