Practice Questions for Algebra - Quadratic Equations

1. CRE 4 - Two Quadratic Equations | Algebra - Quadratic Equations

Form another quadratic equation whose roots are 2 more than the roots of the quadratic equation 2x² + 3x + 1 = 0

2. CRE 4 - Two Quadratic Equations | Algebra - Quadratic Equations

Form another quadratic equation whose roots are 1 less than the roots of the quadratic equation 2x² + 3x + 1 = 0

3. CRE 4 - Two Quadratic Equations | Algebra - Quadratic Equations

Form another quadratic equation whose roots are twice the roots of the quadratic equation 2x² + 3x + 1 = 0

4. CRE 4 - Two Quadratic Equations | Algebra - Quadratic Equations

If α and β are the roots of the equation 2x² + 3x + 1 = 0, then form another quadratic equation whose roots are α² and β²

5. CRE 4 - Two Quadratic Equations | Algebra - Quadratic Equations

Form another quadratic equation whose roots are reciprocal of the quadratic equation 3x² - 11x + 13 = 0.

Answer: Option C

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Explanation :

To form a quadratic equation whose roots are reciprocal of the roots of ax² + bx + c = 0, we substitute x with 1/x in this equaiton.

∴ The required equation is

3 ${(\frac{1}{x})}^{2}$ - 11 $(\frac{1}{x})$ + 13 = 0

⇒ 3 - 11x + 13x² = 0

⇒ 13x² - 11x + 3 = 0

Hence, option (c).

6. CRE 4 - Two Quadratic Equations | Algebra - Quadratic Equations

Form a quadratic equation whose roots are equal in magnitude but opposite in sign to the roots of 2x² - 3x - 6 = 0

CRE 4 - Two Quadratic Equations | Algebra - Quadratic Equations