Question

if the sum and difference of the zeros of a quadratic polynomials are-3 and -10 respectively, find the difference of squares of zeros ​

Answer 1

AnswEr:-

The Required Answer Is 30.

ExplanaTion:-

Given:-

• Sum of the zeroes of a quadratic polynomial = (-3).

• Difference Of the zeroes of the quadratic polynomial = (-10).

To Find:-

• The difference 0f squares of the zeroes.

ID Used:-

$\red{\bullet \boxed{ \pink{ \bf {a}^{2} - {b}^{2} = (a + b)(a - b).}}}$

So Now,

Let the zeroes of the quadratic polynomial be 'x' and 'y'.

So According To The Question:-

$\orange{ \bf\longrightarrow x + y = ( - 3)}...(1)$

And,

$\orange{\bf\longrightarrow x - y = ( - 10)}...(2)$

And we have to find out the value of $\bf x^2 - y^2.$

Therefore by ID:-

$\red{\bullet \boxed{ \blue{\bf {x}^{2} - {y}^{2} = (x + y)(x - y).}}}$

So From (1) and (2) we get,

$\tt\mapsto {x}^{2} - {y}^{2} = ( - 3) \times ( - 10).$

$\large\pink{\mapsto \boxed{ \orange{ \bf{x}^{2} - {y}^{2} = 30.}}}$

$\bf\therefore$ The difference of the squares of the zeroes is equal to 30.

More Related Information:-

• If we have a quadratic polynomial $\bf ax^2+bx+c.$

• Then the sum of its zeroes would always equals to $\bf-\dfrac{b}{a}.$

• And the product of zeroes would always equals to $\bf\dfrac{c}{a}.$

• A quadratic polynomial, always have only 2 zeroes.

• The degree of a quadratic polynomial is always equals to 2.

• So we can say that degree of a polynomial = Number of its zeroes.

Answer 2

Answer:

Step-by-step explanation: