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Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?
Concept: Fundamental Theorem of Arithmetic
(HCF × LCM) for the numbers 70 and 40 is ______.
Concept: Fundamental Theorem of Arithmetic
If HCF (72, 120) = 24, then LCM (72, 120) is ______.
Concept: Fundamental Theorem of Arithmetic
Find the zeroes of the quadratic polynomial 4x2 – 4x + 1 and verify the relation between the zeroes and the coefficients.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is ______.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
The number of quadratic polynomials having zeroes –5 and –3 is ______.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
The zeroes of the polynomial 3x2 + 11x – 4 are ______.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
If one zero of the polynomial p(x) = 6x2 + 37x – (k – 2) is reciprocal of the other, then find the value of k.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to ______.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
Find the zeroes of the quadratic polynomial x2 + 6x + 8 and verify the relationship between the zeroes and the coefficients.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
The zeroes of the quadratic polynomial 16x2 – 9 are ______.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
A fraction becomes `(1)/(3)` when 2 is subtracted from the numerator and it becomes `(1)/(2)` when 1 is subtracted from the denominator. Find the fraction.
Concept: Algebraic Methods of Solving a Pair of Linear Equations >> Elimination Method
A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.
Concept: Algebraic Methods of Solving a Pair of Linear Equations >> Elimination Method
Solve for x: `sqrt(3x^2)-2sqrt(2)x-2sqrt3=0`
Concept: Nature of Roots of a Quadratic Equation
Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.
Concept: Nature of Roots of a Quadratic Equation
For what value of k, the roots of the equation x2 + 4x + k = 0 are real?
Concept: Nature of Roots of a Quadratic Equation
Find the value of k for which the roots of the equation 3x2 – 10x + k = 0 are reciprocal of each other.
Concept: Nature of Roots of a Quadratic Equation
Which of the following equations has 2 as a root?
Concept: Nature of Roots of a Quadratic Equation
Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)2 = 0 has real and equal roots.
Concept: Nature of Roots of a Quadratic Equation
‘The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages.
Concept: Nature of Roots of a Quadratic Equation
