Please select a subject first
Advertisements
Advertisements
If -5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x)k = 0 has equal roots, find the value of k.
Concept: Nature of Roots of a Quadratic Equation
If (k – 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value of k.
Concept: Nature of Roots of a Quadratic Equation
Find the value of k for which the following equation has equal roots.
x2 + 4kx + (k2 – k + 2) = 0
Concept: Nature of Roots of a Quadratic Equation
The 4th term of an A.P. is 22, and the 15th term is 66. Find the first term and the common difference. Hence, find the sum of the series to 8 terms.
Concept: Nature of Roots of a Quadratic Equation
Solve for x using the quadratic formula. Write your answer corrected to two significant figures. (x - 1)2 - 3x + 4 = 0
Concept: Nature of Roots of a Quadratic Equation
Solve the following equation:
`x - 18/x = 6` Give your answer correct to two significant figures.
Concept: Nature of Roots of a Quadratic Equation
Without solving the following quadratic equation, find the value of ‘p’ for which the roots are equal.
px2 – 4x + 3 = 0
Concept: Nature of Roots of a Quadratic Equation
If 3 is a root of the quadratic equation x2 – px + 3 = 0, then p is equal to ______.
Concept: Nature of Roots of a Quadratic Equation
Solve the following quadratic equation:
x2 + 4x – 8 = 0
Give your Solution correct to one decimal place.
(Use mathematical tables if necessary.)
Concept: Nature of Roots of a Quadratic Equation
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
Concept: Nature of Roots of a Quadratic Equation
The roots of quadratic equation x2 – 1 = 0 are ______.
Concept: Nature of Roots of a Quadratic Equation
If b is the mean proportion between a and c, show that: `(a^4 + a^2b^2 + b^4)/(b^4 + b^2c^2 + c^4) = a^2/c^2`.
Concept: Proportion
If (3a + 2b) : (5a + 3b) = 18 : 29. Find a : b
Concept: Ratio
The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series
Concept: Ratio
Using properties of proportion, solve for x. Given that x is positive:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
Concept: Proportion
Calculate the ratio in which the line joining A(−4, 2) and B(3, 6) is divided by point P(x, 3). Also, find
- x
- length of AP.
Concept: Ratio
If (x - 9) : (3x + 6) is the duplicate ratio of 4: 9, find the value of x.
Concept: Ratio
What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?
Concept: Proportion
Using the properties of proportion, solve for x, given `(x^4 + 1)/(2x^2) = 17/8`.
Concept: Proportion
The monthly pocket money of Ravi and Sanjeev are in the ratio 5 : 7. Their expenditures are in the ratio 3 : 5. If each saves Rs. 80 every month, find their monthly pocket money.
Concept: Ratio
