Question

Find the zeros of the quadratic polynomial x square - 3x- 10 and verify the relationship between the zeros and the coefficient

Answer 1

SOLUTION:-

Given:

•Quadratic polynomial is x² -3x -10. &

Verify relationship between the zeros & the coefficient.

To find:

The zeros of the polynomial.

Explanation:

Factorise: x² -3x -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

Alpha = 5 & Beta=-2

The relationship between the zeros & coefficient;

Now,

•Ax² + Bx +C =0 compare with the polynomial.

•A = 1

•B= -3

•C= -10

⚫Sum of zeros:

$= > \alpha + \beta = 5 + ( - 2) \\ \\ = > \alpha + \beta = 5 - 2 = 3 = - \frac{coefficient \: of \: {x}^{2} }{coefficient \: of \: x}$

⚫Product of zeros :

$= > \alpha \beta = 5 \times (- 2 )= - 10 = \frac{contant \: term}{coefficient \: of \: x}$

Thank you.

Answer 2

Step-by-step explanation:

SOLUTION:-

Given:

•Quadratic polynomial is x² -3x -10. &

Verify relationship between the zeros & the coefficient.

To find:

The zeros of the polynomial.

Explanation:

Factorise: x² -3x -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

Alpha = 5 & Beta=-2

The relationship between the zeros & coefficient;

Now,

•Ax² + Bx +C =0 compare with the polynomial.

•A = 1

•B= -3

•C= -10

⚫Sum of zeros:

\begin{gathered}= > \alpha + \beta = 5 + ( - 2) \\ \\ = > \alpha + \beta = 5 - 2 = 3 = - \frac{coefficient \: of \: {x}^{2} }{coefficient \: of \: x}\end{gathered}

=>α+β=5+(−2)

=>α+β=5−2=3=−

coefficientofx

coefficientofx

2

⚫Product of zeros :

= > \alpha \beta = 5 \times (- 2 )= - 10 = \frac{contant \: term}{coefficient \: of \: x}=>αβ=5×(−2)=−10=

coefficientofx

contantterm

Thank you.