Question

40.Find the zeroes of the polynomial ^2+7x +10.and verify the relation between the zeroes and the

coefficients.​

Answer 1

Answer:

p(x) = x²+7x+10

= x²+5x+2x+10

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

= (x+2)(x+5)

x+2 = 0 and x+5 = 0

x = -2 and x = -5

the zeroes are -2 and -5

verification,

take α & β as zeroes of p(x)

α = -2

β = -5

a= 1, b = 7 , c = 10

α+β = -b/a

-2-5 = -7/1

-7 = -7

αβ = c/a

(-2)(-5) = 10/1

10 = 10

Hence, verified ☺

Answer 2

Correct Question:

Find the zeroes of the polynomial

x² + 7x + 10 = 0 and verify the relation between the zeroes and the coefficients.

Answer:

The roots of the given quadratic equation are - 5 or - 2.

Step-by-step-explanation:

The given quadratic equation is x² + 7x + 10 = 0.

➞ x² + 7x + 10 = 0

➞ x² + 5x + 2x + 10 = 0

➞ x ( x + 5 ) + 2 ( x + 5 ) = 0

➞ ( x + 5 ) ( x + 2 ) = 0

➞ x + 5 = 0 or x + 2 = 0

➞ x = - 5 or x = - 2

The roots of the given quadratic equation are - 5 or - 2.

Now, comparing the given quadratic equation to ax² + bx + c = 0, we get,

• a = 1

• b = 7

• c = 10

Now, we know that,

Sum of zeroes = α + β = - b / a

➞ Sum of zeroes = α + β = - 7 / 1

➞ α + β = - 7 / 1

➞ ( - 5 ) + ( - 2 ) = - 7 / 1

➞ - 7 = - 7

Hence verified!

Now, we know that,

Product of zeroes = α.β = c / a

Product of zeroes = α.β = 10 / 1

➞ α.β = 10

➞ ( - 5 ) × ( - 2 ) = 10

➞ 10 = 10

Hence verified!

Additional Information:

1. Quadratic Equation :

An equation having a degree '2' is called quadratic equation.

The general form of quadratic equation is

ax² + bx + c = 0

Where, a, b, c are real numbers and a ≠ 0.

2. Roots of Quadratic Equation:

The roots means nothing but the value of the variable given in the equation.

3. Methods of solving quadratic equation:

There are mainly three methods to solve or find the roots of the quadratic equation.

A) Factorization method

B) Completing square method

C) Formula method

4. Formula to solve quadratic equation:

$\boxed{\red{\sf\:x\:=\:\dfrac{-\:b\:\pm\:\sqrt{b^{2}\:-\:4ac}}{2a}}}$