Maths Book back answers and solution for Exercise questions - Find a polynomial equation of minimum degree with rational coefficients

EXERCISE 3.2

1. If *k *is real, discuss the nature of the roots of the polynomial equation 2*x*2 + *kx *+ *k *= 0 , in terms of *k*.

2. Find a polynomial equation of minimum degree with rational coefficients, having 2 + âˆš3*i* as a root.

3. Find a polynomial equation of minimum degree with rational coefficients, having 2*i* + 3 as a root.

4. Find a polynomial equation of minimum degree with rational coefficients, having âˆš5 - âˆš3 as a root.

5. Prove that a straight line and parabola cannot intersect at more than two points.

Answers:

1. When k < 0 , the polynomial has real roots.

When k = 0 or k = 8 , the roots are real and equal.

When 0 < k < 8 the roots are imaginary.

When k > 8 the roots are real and distinct.

2. *x*2 - 4*x* + 7 = 0

3. *x*2 - 6*x* +13 = 0

4. *x*4 -16*x*2 + 4

Tags : Problem Questions with Answer, Solution , 12th Mathematics : UNIT 3 : Theory of Equations

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12th Mathematics : UNIT 3 : Theory of Equations : Exercise 3.2: Polynomial Equation in Geometry | Problem Questions with Answer, Solution

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