Question

If α and β (α < β), are the roots of the equation x2 + bx + c = 0, where c < 0 < b, then

Solution

Correct option is

Given α < β, c is – ive and b = + ive.    

α + β = – b = – ive, αβ = c = – ive     

α < β ⇒ α must be a – ive root and βa + ive root as αβ is – ive

Again α + β < 0 ⇒ β < – α ⇒ β < .

SIMILAR QUESTIONS

Q1

If α, β, γ are the roots of the equation x3 + ax + b = 0, then

 

Q2

Let α, β be the roots of x2 – x + p = 0 and γ, δ be the roots of x2 – 4x + = 0. If α, β, γ, δ are in G.P., then the integral values of p and qrespectively, are

Q3

 

Let P, Q, R be defined as

       P = a2b + ab2 – a2c – ac2,

       Q = b2c + bc2 – a2b – ac2

       R = a2c + c2a – c2b – cb2

Where abc are all + ive and the equation Px2 + Qx + R = 0 has equal roots then abc are in

Q4

Let α and β are the roots of equation x2 + x + 1 = 0. The equation whose roots are α19, β7 is

Q5

If x2 + x + 1 is a factor ax3 + bx2 + cx + d, then the real root of ax3 + bx2cx + d = 0 is

Q6

If one root of the equation (a2 – 5a + 3)x2 + (3a – 1)x + 2 = 0 be double the other, then the value of α is:

Q7

For the equation 3x2 + px + 3 = 0, p > 0, if one of the roots is square of the other, then p is equal to

Q8

If the roots of the equation x2 – 2ax + a2 + a – 3 = 0 are real and less than 3, then

Q9

If b > a, then the equation (x – a) (x – b) – 1 = 0, has

Q10

If 1 lies between the roots of the equation 3x2 – 3 sin α x – 2 cos2 α = 0 then α lies in the interval