Practice Questions for Algebra - Quadratic Equations | CRE 3 - Forming a Quadratic Equation and Relation between roots and coefficients

1. CRE 3 - Forming a Quadratic Equation and Relation between roots and coefficients | Algebra - Quadratic Equations

Form a quadratic equation whose roots at 5 and 6.

(a)
x² – 11x - 30 = 0
(b)
x² – 11x + 30 = 0
(c)
x² + 11x + 30 = 0
(d)
None of these

2. CRE 3 - Forming a Quadratic Equation and Relation between roots and coefficients | Algebra - Quadratic Equations

Form a quadractic equation whose sum of the roots is 2 and product is -15.

(a)
x² – 2x + 15 = 0
(b)
x² + 2x – 15 = 0
(c)
x² – 2x – 15 = 0
(d)
None of these

3. CRE 3 - Forming a Quadratic Equation and Relation between roots and coefficients | Algebra - Quadratic Equations

If α and β are the roots of the equation 2x² - 3x - 5 = 0, then find the value of 1/α + 1/β?

(a)
-3/5
(b)
-2/3
(c)
3/5
(d)
None of these

4. CRE 3 - Forming a Quadratic Equation and Relation between roots and coefficients | Algebra - Quadratic Equations

If α and ß are the roots of the equation x² – 3x + 5 = 0, then what is the value of α³ + ß³?

(a)
18
(b)
-18
(c)
-10
(d)
10

5. CRE 3 - Forming a Quadratic Equation and Relation between roots and coefficients | Algebra - Quadratic Equations

The roots of the quadratic equation 9x² - 36x + a = 0 are in the ratio 2 : 1. Find the value of a.

(a)
16
(b)
32
(c)
32/9
(d)
None of these

6. CRE 3 - Forming a Quadratic Equation and Relation between roots and coefficients | Algebra - Quadratic Equations

Lomror & Rohit attempted to solve a quadratic equation. Lomror made a mistake while noting down the constant term and got the roots as 4 & 3. Rohit made a mistake while noting down the coefficient of x and got the roots as 2 & 3. Find the roots of the actual quadratic equation.

(a)
-1 and -6
(b)
1 and -6
(c)
1 and 6
(d)
None of these

7. CRE 3 - Forming a Quadratic Equation and Relation between roots and coefficients | Algebra - Quadratic Equations

Find the quadratic equation whose one root is 3 + 2√2 and has rational coefficients.

(a)
x² + 6x + 1 = 0
(b)
x² - 6x - 1 = 0
(c)
x² - 6x + 1 = 0
(d)
None of these

CRE 3 - Forming a Quadratic Equation and Relation between roots and coefficients | Algebra - Quadratic Equations

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