Question

If the sum and dofference of zeros of quadratic polynomial are -3 and -10 respectively. Then find the difference of the square of zeros.​

Answer 1

★Given:-

→Sum of Zeros=α+β=-3

→Difference of zeros=α-β=-10

★To find:-

→Difference of the square of zeroes

=α²-β²?

$\rule{200}{1}$

★Proof:-

♦Multiply both Sum and Difference of Zeroes.

→(α+β)×(α-β)=α²-β²

♦Put the Values↓

→α²-β²=-3×-10

→α²-β²=30

$\rule{200}{1}$

↓-OR-↓

$\rule{200}{1}$

α+β=-3--(1)

α-β=-10--(2)

⊗Add them⊗

2α=-13

α=$\frac{-13}{2}$--(3)

★Using (3) in any of the 2 equations★

→$\frac{-13}{2}$+β=-3

⊕Shifting α value to RHS⊕

β=-3+$\frac{13}{2}$

*Cross Multiply in RHS*

β=$\frac{-6+13}{2}$

β=$\frac{7}{2}$

$\rule{200}{1}$

♦Now α²-β²↓

→($\frac{13}{2}$)²-($\frac{7}{2}$)²

→$\frac{169-49}{4}$

α²-β²→$\frac{\cancel{120}}{\cancel{4}}$=30

$\rule{200}{1}$