NCERT Mathematics Class 10 Exemplar Ch 4 Quadratic Equations Part 2

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EXERCISE 4.2

1. State whether the following quadratic equations have two distinct real roots. Justify your answer.

(i) (ii)

(iii) (iv)

(v) (vi)

(vii) (viii)

(ix) (x)

Answer: (i) No, because discriminant =

(ii) Yes, because discriminant =

(iii) No, because discriminant = 0.

(iv) Yes, because discriminant =

(v) No, because discriminant = .

(vi) Yes, because discriminant = .

(vii) Yes, because discriminant = .

(viii) No, because discriminant = .

(ix) Yes, because discriminant = .

(x) Yes, because discriminant = .

2. Write whether the following statements are true or false. Justify your answers.

(i) Every quadratic equation has exactly one root.

(ii) Every quadratic equation has at least one real root.

(iii) Every quadratic equation has at least two roots.

(iv) Every quadratic equation has at most two roots.

(v) If the coefficient of and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

(vi) If the coefficient of and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

Answer: (i) False, for example : is a quadratic equation with two roots.

(ii) False, for example has no real root.

(iii) False, for example : is a quadratic equation which has no real roots.

(iv) True, because every quadratic polynomial has almost two zeroes.

(v) True, because if in , a and c have opposite signs, then and so

(vi) True, because if in , a and c have same sign and , then .

3. A quadratic equation with integral coefficient has integral roots. Justify your answer.

Answer: is an equation with integral coefficients but its roots are not integers.

4. Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

Answer: , which has roots ,

5. Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?

Answer: Yes. , which has roots 3, 4

6. Is 0.2 a root of the equation Justify.

Answer: No

7. If , , is it true that the roots of are numerically equal and opposite in sign? Justify.

Answer: Yes

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