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If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
Concept: Nature of Roots of a Quadratic Equation
Form the quadratic equation if its roots are –3 and 4.
Concept: Nature of Roots of a Quadratic Equation
Solve the quadratic equation 2x2 + 5x + 2 = 0 using formula method.
Concept: Method of Solving a Quadratic Equation>Quadratic Formula (Shreedharacharya's Rule)
If a = 1, b = 8 and c = 15, then find the value of `"b"^2 - 4"ac"`
Concept: Nature of Roots of a Quadratic Equation
From the quadratic equation if the roots are 6 and 7.
Concept: Nature of Roots of a Quadratic Equation
What is the value of discriminant for the quadratic equation X2 – 2X – 3 = 0?
Concept: Nature of Roots of a Quadratic Equation
If roots of a quadratic equation 3y2 + ky + 12 = 0 are real and equal, then find the value of ‘k’.
Concept: Nature of Roots of a Quadratic Equation
Complete the following activity to solve the given quadratic equation by formula method.
2x2 + 13x + 15 = 0
Activity: 2x2 + 13x + 15 = 0
a = (______), b = 13, c = 15
b2 – 4ac = (13)2 – 4 × 2 × (______)
= 169 – 120
b2 – 4ac = 49
x = `(-"b" +- sqrt("b"^2 - 4"ac"))/(2"a")`
x = `(- ("______") +- sqrt(49))/4`
x = `(-13 +- ("______"))/4`
x = `(-6)/4` or x = `(-20)/4`
x = (______) or x = (______)
Concept: Method of Solving a Quadratic Equation>Quadratic Formula (Shreedharacharya's Rule)
If the roots of the given quadratic equation are real and equal, then find the value of ‘m’.
(m – 12)x2 + 2(m – 12)x + 2 = 0
Concept: Nature of Roots of a Quadratic Equation
If `(5sqrt(2) + 3sqrt(3)) - (6sqrt(2) - 7sqrt(3)) = asqrt(2) + bsqrt(3)`, then find a and b.
Concept: Method of Solving a Quadratic Equation>Quadratic Formula (Shreedharacharya's Rule)
Solve: 7x2 – 30x – 25 = 0
Concept: Method of Solving a Quadratic Equation>Quadratic Formula (Shreedharacharya's Rule)
Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax2 + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.
Concept: Nature of Roots of a Quadratic Equation
Solve the quadratic equation: 16x2 + 24x + 9 = 0.
Concept: Method of Solving a Quadratic Equation>Quadratic Formula (Shreedharacharya's Rule)
Solve the quadratic equation 7x2 + 9x + 2 = 0 by the quadratic formula.
Concept: Method of Solving a Quadratic Equation>Quadratic Formula (Shreedharacharya's Rule)
Solve the following quadratic equation by the formula method:
x2 + 10x + 2 = 0
Concept: Method of Solving a Quadratic Equation>Quadratic Formula (Shreedharacharya's Rule)
Solve the following quadratic equation by formula method:
3m2 − m − 10 = 0
Concept: Method of Solving a Quadratic Equation>Quadratic Formula (Shreedharacharya's Rule)
Write an A.P. whose first term is a and the common difference is d in the following.
a = 10, d = 5
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Given Arithmetic Progression 12, 16, 20, 24, . . . Find the 24th term of this progression.
Concept: General Term (nth) of an Arithmetic Progression
In an A.P. 17th term is 7 more than its 10th term. Find the common difference.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
