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The prime factorisation of the number 2304 is ______.
Concept: Fundamental Theorem of Arithmetic
If n is a natural number, then 8n cannot end with digit
Concept: Fundamental Theorem of Arithmetic
The HCF of the smallest 2-digit number and the smallest composite number is ______.
Concept: Fundamental Theorem of Arithmetic
Find all zeroes of the polynomial `(2x^4 - 9x^3 + 5x^2 + 3x - 1)` if two of its zeroes are `(2 + sqrt3)` and `(2 - sqrt3)`
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
Find the sum and product of the roots of the quadratic equation 2x2 – 9x + 4 = 0.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
The graph of y = f(x) is shown in the figure for some polynomial f(x).
The number of zeroes of f(x) is ______.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
Find a quadratic polynomial whose zeroes are 6 and – 3.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
Find the zeroes of the polynomial x2 + 4x – 12.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
Read the following passage:
Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 Students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively. |
Based on the above information, answer the following questions:
- Represent the following information algebraically (in terms of x and y).
- (a) What is the prize amount for hockey?
OR
(b) Prize amount on which game is more and by how much? - What will be the total prize amount if there are 2 students each from two games?
Concept: Algebraic Methods of Solving a Pair of Linear Equations >> Elimination Method
If the quadratic equation px2 − 2√5px + 15 = 0 has two equal roots then find the value of p.
Concept: Nature of Roots of a Quadratic Equation
If `x=2/3` and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
Concept: Nature of Roots of a Quadratic Equation
If x=−`1/2`, is a solution of the quadratic equation 3x2+2kx−3=0, find the value of k
Concept: Nature of Roots of a Quadratic Equation
Solve the quadratic equation 2x2 + ax − a2 = 0 for x.
Concept: Nature of Roots of a Quadratic Equation
The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is `29/20`. Find the original fraction.
Concept: Method of Solving a Quadratic Equation
Find the roots of the following quadratic equation by factorisation:
`sqrt2 x^2 +7x+ 5sqrt2 = 0`
Concept: Method of Solving a Quadratic Equation
Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots.
Concept: Nature of Roots of a Quadratic Equation
The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.
Concept: Method of Solving a Quadratic Equation
Solve for x:
4x2 + 4bx − (a2 − b2) = 0
Concept: Method of Solving a Quadratic Equation
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.
Concept: Method of Solving a Quadratic Equation
