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Draw a histogram of the following data.
| Height of student (cm) | 135 - 140 | 140 - 145 | 145 - 150 | 150 - 155 |
| No. of students | 4 | 12 | 16 | 8 |
Concept: Histograms
The following frequency distribution table shows marks obtained by 180 students in Mathematics examination.
| Marks | No. of students |
| 0 - 10 | 25 |
| 10 - 20 | x |
| 20 - 30 | 30 |
| 30 - 40 | 2x |
| 40 - 50 | 65 |
Find the value of x. Also draw a histogram representing the above information.
Concept: Histograms
Find the values of k for which the quadratic equation 9x2 - 3kx + k = 0 has equal roots.
Concept: Nature of Roots of a Quadratic Equation
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 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
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
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)
