The roots of the equation $x^{2} - p x + q = 0$ are consecutive integers. Find the discriminate of the equation.

- 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $1$
For the given equation, let the roots be $a, a + 1$
So sum of roots $= a + a + 1 = 2 a + 1 = - \frac{- p}{1} = p$
Product of roots $= a \times (a + 1) = a^{2} + a = \frac{q}{1} = q$
For an equation $a x^{2} + b x + c = 0$ , the discriminant is $b^{2} - 4 a c$ .
For the given eqn, the discriminant is ${(- p)}^{2} - 4 \times 1 \times q = (2 a + 1)^{2} - 4 (a^{2} + a) = 4 a^{2} + 1 + 4 a - 4 a^{2} - 4 a = 1$

Suggest Corrections

Similar questions

If $x^{2}$ +px + q = 0 is the quadratic equation whose roots are a – 2 and b – 2 where a and b are the roots of $x^{2}$ - 3x + 1 =0, then

Q. The roots of equation

x^{2} + p x + q = 0

are

1

and

2

. The roots of the equation

q x^{2} - p x + 1 = 0

must be

Q. If

α & β

are the roots of equation.

x^{2} + p x + q = 0

, then -

- \frac{1}{α}, - \frac{1}{β}

are the roots of the equation.

If $α, β$ are the roots of the equation $x^{2} + p x + 1 = 0; γ, δ$ the roots of the equation $x^{2} + p x + 1 = 0;$ then $(α - γ) (α + δ) (β - γ) (β + δ)$

Q. If the roots of

x^{2} - p x + q = 0

are two consecutive integers, find the value of

p^{2} - 4 q .

Join BYJU'S Learning Program

The roots of the equation x2−px+q=0 are consecutive integers. Find the discriminate of the equation.

The correct option is B 1For the given equation, let the roots be a,a+1So sum of roots =a+a+1=2a+1=−−p1=pProduct of roots =a×(a+1)=a2+a=q1=qFor an equation ax2+bx+c=0, the discriminant is b2−4ac.For the given eqn, the discriminant is (−p)2−4×1×q=(2a+1)2−4(a2+a)=4a2+1+4a−4a2−4a=1

The roots of the equation $x^{2} - p x + q = 0$ are consecutive integers. Find the discriminate of the equation.