Question

Find the zeroes of the quadratic polynomial x

ଶ − 3x − 10 and verify the

relationship between the zeroes and coefficient.​

Answer 1

Step-by-step explanation:

x²-3x-10

x²-5x+2x-10

x(x-5)+2(x-5)

(x-5)(x+2)

x=5,x-2

α+β=-b/a

5-2=3/1

3=3

αβ=c/a

5(-2)=-10/1

-10=-10

Answer 2

The zeros of the quadratic equation are x = -2 and x = 5

Solution:

Given equation is:

$x^2 - 3x - 10$

We have to find the zeros of the quadratic equation

$x^2 - 3x - 10 = 0$

$\text{Split the middle term } \\\\x^2 + 2x - 5x - 10 = 0\\\\\mathrm{Break\:the\:expression\:into\:groups}\\\\\left(x^2+2x\right)+\left(-5x-10\right) = 0\\\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+2x\mathrm{:\quad } \\\\x(x + 2) + (-5x-10) = 0\\\\\mathrm{Factor\:out\:}-5\mathrm{\:from\:}-5x-10\mathrm{:\quad } \\\\x\left(x+2\right)-5\left(x+2\right) = 0 \\\\\mathrm{Factor\:out\:common\:term\:}x+2\\\\\left(x+2\right)\left(x-5\right) = 0\\\\Thus\ the\ zeros\ are \\\\x = -2\\\\x = 5$

Thus:

Sum of zeros = -2 + 5 = 3

Product of zeros = -2 x 5 = -10

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