Quadratic equations 2 p-1 z2-2 p-1 z-c-0 and q-1 y2-4 q-1 y-3 c-0 have the same pair of roots- Given that -0- what is the value of p-q -A- 4B- 2C- Cannot be determinedD- 3

The correct option is D 3For the equations to have same pair of roots 2p 1/q+1=2p+1/4q+1=c/3c ∴ 3(2p 1)=q+1 ⇒ 6p q=4 and, 3(2p+1)=4q+1 ⇒ 6p 4q= 2 Solving two e ...

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Quantitative Aptitude

Quadratic Equations

Quadratic equ...

Question

Quadratic equations $(2 p - 1) z^{2} + (2 p + 1) z + c = 0$ and $(q + 1) y^{2} + (4 q + 1) y + 3 c = 0$ have the same pair of roots. Given that $c \neq 0$ , what is the value of (p+q)?

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Cannot be determined

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Solution

The correct option is A 3
For the equations to have same pair of roots
$\frac{2 p - 1}{q + 1} = \frac{2 p + 1}{4 q + 1} = \frac{c}{3 c}$
$∴ 3 (2 p - 1) = q + 1 \Rightarrow 6 p - q = 4$
and, $3 (2 p + 1) = 4 q + 1 \Rightarrow 6 p - 4 q = - 2$
Solving two equation q = 2 and p =1
$∴ (p + q) = 3$

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Quadratic equations (2p−1)z2+(2p+1)z+c=0 and (q+1)y2+(4q+1)y+3c=0 have the same pair of roots. Given that c≠0, what is the value of (p+q)?

The correct option is A 3For the equations to have same pair of roots 2p−1q+1=2p+14q+1=c3c ∴3(2p−1)=q+1⇒6p−q=4 and, 3(2p+1)=4q+1⇒6p−4q=−2 Solving two equation q = 2 and p =1 ∴(p+q)=3

Quadratic equations $(2 p - 1) z^{2} + (2 p + 1) z + c = 0$ and $(q + 1) y^{2} + (4 q + 1) y + 3 c = 0$ have the same pair of roots. Given that $c \neq 0$ , what is the value of (p+q)?

The correct option is A 3
For the equations to have same pair of roots
$\frac{2 p - 1}{q + 1} = \frac{2 p + 1}{4 q + 1} = \frac{c}{3 c}$
$∴ 3 (2 p - 1) = q + 1 \Rightarrow 6 p - q = 4$
and, $3 (2 p + 1) = 4 q + 1 \Rightarrow 6 p - 4 q = - 2$
Solving two equation q = 2 and p =1
$∴ (p + q) = 3$