Question

Construct a parallelogram PQRS if mPQ = 7.5cm , MZQ = 120° and MQR = 5.5cm. Construct angle with the help of compass. Steps of construction ​

Answer 1

Answer:

Given that, α and β are the zeroes of the polynomial x^2 + 5x + c.

We know, a^2x + bx + c = 0.

By comparing both we get :-

a = 1

b = 5

c = c

Given,

: \implies \sf \alpha - \beta = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: ...(1):⟹α−β=3...(1)

Sum of zeroes :-

: \implies \sf \alpha + \beta = - \dfrac{b}{a}:⟹α+β=−

a

b

: \implies \sf \alpha + \beta = - \dfrac{5}{1}:⟹α+β=−

1

5

: \implies \sf \alpha + \beta = - 5 \: \: \: \: \: \: \: \: \: \: \: \: \: ...(2):⟹α+β=−5...(2)

Product of zeroes :-

: \implies \sf \alpha \times \beta = \dfrac{c}{a}:⟹α×β=

a

c

: \implies \sf \alpha \times \beta = c\: \: \: \: \: \: \: \: \: \: \: \: \: ...(3):⟹α×β=c...(3)

By adding eq(1) and eq(2) we get :-

: \implies \sf 2 \alpha = - 2:⟹2α=−2

: \implies \sf \alpha = - 1:⟹α=−1

By substituting α = -1 in eq(1) we get :-

: \implies \sf - 1 + \beta = - 5:⟹−1+β=−5

: \implies \sf \beta = - 4:⟹β=−4

Now substitute the value of α and β in eq(3) :-

: \implies \sf - 1 \times - 4 = c:⟹−1×−4=c

: \implies \bf c = 4:⟹c=4

Answer :- Option C