# top-nda&cds maths paper qustion in dehradunQuestion

**nda&cds maths paper qustion in dehradunQuestion**

**1**. State which all quadratic equations have real roots, no real roots

- x
^{2}+ x+7=0 - 3x
^{2}+6x+1=0 - 9x
^{2}+x +3=0 - 11x
^{2}-12x-1=0 - -13x
^{2}+3x+7=0 - 2x
^{2}-6x+3=0 - x-(1/x)-3=0 x≠0
- –x
^{2}-2x-2=0

**Solution **

__Nature of roots of Quadratic equation__

S.no | Condition | Nature of roots |

1 | b^{2} -4ac > 0 |
Two distinct real roots |

2 | b^{2}-4ac =0 |
One real root |

3 | b^{2}-4ac < 0 |
No real roots |

Real roots: : (b), (d) ,(e),(f),(g)

No real roots : (a) ,(c),(h)

**Question 2**. Find the roots of the quadratic equation using factorization technique

a) x^{2}-3x-10=0

b) x^{2} -11x+30=0

**Solution**

a)

x^{2} -5x+2x-10=0

x(x-5) +2(x-5)=0

(x+2)(x-5)=0

So roots are x=-2 and 5

b) Roots are 5 and 6

**Question 3.** Find the roots of the quadratic equation using square method

a) x^{2} +4x-5=0

b) 2x^{2}-7x+3=0

Solution

a)

(x+4/2)^{2} –(4/2)^{2} -5=0

(x+2)^{2}-9=0

(x+2)^{2}=9

x+2=±3

x=1 or -5

b)

(x-7/4)^{2} -(7/4)^{2} +3/2=0

(x-7/4)^{2}=49/16 -3/2

(x-7/4)^{2}=25/16

x-7/4=±5/4

or

x=1/2 or 3

**Question 4** –**True or False statement**

a) There are no reals roots of the quadratic equation x^{2}+4x+5=0

b) The roots of the equation x^{2}-1=0 are 1,-1

c) A quadratic equation can have at most 2 real roots

d) In a quadratic equation ax^{2} +bx+c=0 ,if a and c are of same sign and b is zero ,the quadratic equation has real roots

e) In a quadratic equation ax^{2} +bx+c=0 ,if a and c are of opposite sign, then quadratic equation will definitely have real roots

f) for k > 0,the quadratic equation 2x^{2}+6x-k=0 will definitely have real roots

g) if the roots of the quadratic equation are rational, the coefficient of the term x will also be rational.

h) if the roots of the quadratic equation are irrational, the coefficient of the term x will also be irrational

I) Every quadratic equation will have rational roots

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