Quadratic Equation [BCB Ex6.1]

Posted on August 16, 2023December 27, 2023 by MEAN

Determine the nature of roots of each of the following equations
1. $x^2-6x+5=0$
  
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  Solution :1a
2. $x^2-4x-3=0$
  
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  Solution :1b
3. $x^2-6x+9=0$
  
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  Solution :1c
4. $4x^2-4x+1=0$
  
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  Solution :1d
5. $2x^2-9x+35=0$
  
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  Solution :1e
6. $4x^2+8x-5=0$
  
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  Solution :1f
For what values of p will the equation $5x^2-px+45=0$ ?

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Solution :2
if the equation $x^2+2(k+2)x+9k=0$ has equal roots, find k.

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Solution :3
For what value of a will the equation $x^2-(3a-1)x+2(a^2-1)=0$ have equal roots?

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Solution :4
If the roots of the equation $(a^2+b^2)x^2-2(ac+bd)x+(c^2+d^2)=0$ are equal, then show that $\frac{a}{b}=\frac{c}{d}$

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Solution :5
Show that the roots of the equation $(a^2-bc)x^2+2(b^2-ca)x+(c^2-ab)=0$ will be equal, if either $b=0$ or $a^3+b^3+c^3-3abc=0$

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Solution :6
If $a,b,c$ are rational and $a+b+c=0$ , show that the roots $(b+c-a)x^2+(c+a-b)x+(a+b-c)=0$ are rational.

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Solution :7
Prove that the roots of the equation $(x-a)(x-b)=k^2$ are real for all values of k.

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Solution :8
Show that the roots of the equation $x^2-4abx+(a^2+2b^2)^2=0$ are imaginary.

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Solution :9
If the roots of the quadratic equation $qx^2+2px+2q=0$ are real and unequal, prove that the roots of the equation $(p+q)x^2+2qx+(p-q)=0$ are imaginary

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Solution :10

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