Q28 of 27 Page 1

If one root of the quadratic equation 3x2 + px + 4 = 0 is 2/3, then find the value of p and the other root of the equation.

OR


The roots α and β of the quadratic equation x2 - 5x + 3(k - 1) = 0 are such that α – β = 1. Find the value of k.


3x2 + px + 4 = 0


3(2/3)2 + p(2/3) + 4 = 0


4/3 + 2p/3 + 4 = 0


p = -8


3x2 - 8x + 4 = 0


By middle term splitting,


3x2 - 6x - 2x + 4 = 0


x = 2/3 or x = 2


Hence, x = 2


OR


α + β = 5 ----(1)


α – β = 1 ----(2)


Solving (1) and (2), we get


α = 3 and β = 2


also, αβ = 6


or 3(k - 1) = 6


k – 1 = 2


k = 3


More from this chapter

All 27 →
25

If tanA = 3/4, find the value of 1/sinA + 1/cosA

OR


If √3 sinƟ-cosƟ=0 and 0°<Ɵ <90°, find the value of Ɵ


 27

Prove that 2-√3 is irrational, given that √3 is irrational.

 29

In the figure, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region.


 30

The perimeters of two similar triangles are 25cm and 15cm respectively. If one side of the first triangle is 9cm, find the length of the corresponding side of the second triangle.

OR


In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC. Prove that 9 AD2 = 7 AB2.