## Condition for common roots - Basic

In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no term.

Q1.  If equations x2+bx+a=0 and x2+ax+b=0 have one root common and a is not equal to 0 , then

•   a-b=1
•  a+b=0
•  a+b=-1
•  a-b=1

a+b=-1

Q2.  If x2+ax+10=0 and x2+bx-10=0 have a common root, then a2-b2 is equal to

•  t210
•  t220
•  t230
•  t240

40

Q3.  If ax2+bx+c=0 and bx2+cx+a=0 have a common root and a is not equal to , then (a3+b3+c3)/abc = given by

•   1
•  2
•  3
•   None of these

3

Q4.  If the equation x2+px+q=0 and x2+qx+p=0, have a common root, then p+q+1=

•   0
•   1
•  2
•  None of these

0

Q5.  If the roots of a1x2+b1x+c1 and a2x2+b2x+c2 are the same, then

•  a1=a2, b1=b2, c1=c2
•  c1=c2=0
•  a1/a2 = b1/b2 = c1/c2
•  None of these

a1/a2 = b1/b2 = c1/c2

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