Quadratic Equation (One Variable)

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

Click on each question to see answer & solution.

Question No: #51

If the common root of the equations `x^2+ax+8=0` and `x^2+bx+a=0` is `2`, then find the value of `a` and `b`.
Ans: `a=-6, b=1`
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Question No: #52

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: #53

If the ratio of roots of the equation `ax^2+bx+c=0` is `1:r`, then show that, `\frac{(r+1)^2}{r} = \frac{b^2}{ac}`.

Question No: #54

If the sum of the roots of the equation `x^2−px+q=0` be three times of their difference, then show that, `2p^2 = 9q` .

Question No: #55

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: #56

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: #57

If the roots of the equation `a(b-c)x^2+b(c-a)x+c(a-b)=0` are equal, then prove that, `1/a + 1/c = 2/b`.

Question No: #58

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

Question No: #59

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

Question No: #60

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