Question

Verify the relationship between zeroes and coefficients of the polynomials. x2+3x-10

Answer 1

$\mathtt{\huge{\underline{\red{Question\:?}}}}$

✴ Verify the relationship between zeroes and coefficients of the polynomials. x²+3x-10

$\mathtt{\huge{\underline{\green{Answer:-}}}}$

✏ The zeros of polynomials are 2 & 5.

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Given :-

• A quadratic polynomial x²+3x-10 .

To Find :-

• The relationship between zeroes and coefficients of the polynomials.

Calculation :-

Let p(x) be x²+3x-10

To find the zeros of polynomials,

p(x) = 0 .........(1)

We know,

p(x) = x²+3x-10 ............(2)

From 1 & 2 ,

▶ p(x) = x²-3x-10

▶ p(x) = 0

We get,

x²+ 3x-10 = 0

Using middle term factorisation.

↗ x² +(5x-2x)-10 = 0

↗ x² + 5x+2x-10 = 0

↗ x(x+5)-2(x-5) =0

➡ (x-5)(x-2) = 0

(x-5) = 0 & (x-2) = 0

➡ x = 5 & x = 2

So, The zeros of polynomials are 2 & 5 .

Verify the relationship :-

Sum of zeroes :- $\dfrac{-Coefficient\:of\:x}{Coefficient\:of\:x²}$

= $\dfrac{-(-3)}{1}$

3 = 3

It is correct.

Product of zeroes :-$\dfrac{Constant\:term}{Coefficient\:of\:x²}$

= $\dfrac{-10}{1}$

= -10=-10

It is correct.

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Answer 2

⭐Answer⭐

x²+ 3x-10

= x² +(5x-2x)-10

= x² + 5x+2x-10

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

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

x=5 & x=2

Sum of zeroes = α+β = 5-2 = 3

α+β = -b/a = -(-3)/1 = 3

Product of zeroes = αβ = 5*-2 = -10

αβ = c/a = -10/1 = -10

Hence Proved.!

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