Worksheet – 1
Class X
Quadratic Equations
Answer the following questions:
1. Find the values of p such that the quadratic equation px2+6x+1=0 has no real roots.
2. For what value of p does the quadratic equation px2+(p-1)x+(p-1)=0 has repeated roots.
3. Without finding the roots, comment on the nature of the roots of the quadratic equation
9x2-6x+1=0.
4. Find the discriminant of the quadratic equation 3√3x2+10x+√3=0 .
5. Represent the following situation as a quadratic equation:
A motorboat whose speed is 18 km/h in still water takes 1 hour more to go 24km upstream than to
return downstream to the same spot. Find the speed of the stream.
Write true or false:
1
2
3
4
5
Every quadratic equation has at least two roots.
Every quadratic equation has at most two roots.
Every quadratic equation has exactly one root.
If the coefficient of x2 and the constant term of a quadratic equation have opposite signs,
then the quadratic equation has real roots.
If -4 is a root of the equation x2-px-4=0 and x2+px+q=0 has equal roots, then the value of q is
9/4.
Fill in the blanks:
2
3
4
5
6
The condition that one of the roots of the equation ax2+bx+c=0 may be reciprocal of the
other is ……
If one roots of the equation 2x2+px+4=0 is 2 , then the other root is ………
If the roots of the equation (b-c)x2+(c-a)x+(b-c)=0 are equal , then 2b=………
If x=2 is common root of the quadratic equation px2-3px-4=0 and 2x2+x+q=0 then p+q=……….
The least positive value of k for which x2+kx+16=0 has real roots ,is……………….
If the sum of the roots of the quadratic equation is 6 and the product of the roots is 6, then
the quadratic equation is………………………….
Choose the correct answer:
1
For what value of k ,x= √5 is a solution of the equation k x2+√5x-15=0?
1
a)k=2
b) k=0
c)k=2
d)k=√2
2 The values of p for which the quadratic equation 4x2-3px+9=0 has equal roots is
a)p≥-4
b)p==3,-3
c)p≤3
d)-4<p<4
3 The discriminant of the quadratic equation is √2x2 -3√5x + √18 = 0 is
a)2 √6
b)25 c)21
d)36