Maths Book back answers and solution for Exercise questions - Mathematics : Theory of Equations: Vietaâ€™s Formulae and Formation of Polynomial Equations : Exercise problems with Questions, Answers, Solution, Explanation

EXERCISE 3.1

1. If the sides of a cubic box are increased by 1, 2, 3 units respectively to form a cuboid, then the volume is increased by 52 cubic units. Find the volume of the cuboid.

2. Construct a cubic equation with roots

(i) 1, 2 , and 3 (ii) 1,1, and -2 (iii) 2, 1/2 and 1

3. If *Î± *, *Î² *and *Î³ *are the roots of the cubic equation *x*3 + 2*x*2 + 3*x *+ 4 = 0 , form a cubic equation whose roots are

(i) 2Î± , 2Î² , 2Î³

(ii) 1/Î±, 1/Î², 1/Î³

(iii) âˆ’Î± , âˆ’Î² , âˆ’Î³

4. Solve the equation 3*x*3 - 16*x*2 + 23*x *- 6 = 0 if the product of two roots is 1.

5. Find the sum of squares of roots of the equation 2*x*4 - 8*x*3 + 6*x*2 - 3 = 0 .

6. Solve the equation *x*3 - 9*x*2 +14*x *+ 24 = 0 if it is given that two of its roots are in the ratio 3 : 2 .

7. If *Î± *, *Î² *, and *Î³ *are the roots of the polynomial equation *ax*3 + *bx*2 + *cx *+ *d *= 0 , find the value of in terms of the coefficients.

8. If *Î± *, *Î² *,*Î³ *, and *Î´ *are the roots of the polynomial equation 2*x*4 + 5*x*3 - 7*x*2 + 8 = 0, find a quadratic equation with integer coefficients whose roots are *Î± *+ *Î² *+ *Î³ *+ *Î´ *and *Î±Î²Î³Î´ *.

9. If *p *and *q *are the roots of the equation *lx*2 + *nx *+ *n *= 0 , show that

10. If the equations *x*2 + *px *+ *q *= 0 and *x*2 + *pâ€™x *+ *q*â€™ = 0 have a common root, show that it must be equal to

11. Formalate into a mathematical problem to find a number such that when its cube root is added to it, the result is 6 .

12. A 12 metre tall tree was broken into two parts. It was found that the height of the part which was left standing was the cube root of the length of the part that was cut away. Formulate this into a mathematical problem to find the height of the part which was cut away.

Answers:

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12th Mathematics : UNIT 3 : Theory of Equations : Exercise 3.1: Vietaâ€™s Formulae and Formation of Polynomial Equations | Problem Questions with Answer, Solution

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