Quadratic Equation (One Variable)

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #31

Find the values of `p`, for which the quadratic equation `x^2+(p-3)x+p=0` has real and equal roots.

Question No: #32

If the roots of the quadratic equation `(1+m^2)x^2+2mcx+(c^2-p^2)=0` are real and equal, then prove that `c^2=p^2(1+m^2)`.

Question No: #33

Show that, for `a=b`, the equation `2(a^2+b^2)x^2+2(a+b)x+1=0` has no real roots.

Question No: #34

If the equations `x^2+px+r=0` and `x^2+rx+p=0` (`p \ne r`) have a common root, then find the value of `1+p+r`.

Question No: #35

If one of the roots of the equation `x^2+px+12=0` is `2` and two roots of the equation `x^2+px+q=0` are equal, then find the value of `q`.

Question No: #36

In the quadratic equation `ax^2+bx+c=0` (`a\ne0`), if one root is double to other root, then prove that `2b^2=9ac`.

Question No: #37

If two roots of the equation `(b-c)x^2+(c-a)x+(a-b)=0` are equal, then prove that `2b=a+c`.

Question No: #38

Find the equation whose roots are reciprocal of the roots of `2x^2+5x+3=0`.

Question No: #39

Find the equation whose roots are square of the roots of `x^2+x+1=0`.

Question No: #40

Find the equation whose roots are square of the roots of `2x^2+3x+1=0`