Multiple choice

If $A,B$ are roots of the quadratic equation $x^2-5x+6=0$ then the equation whose roots are $A+3$ and $B+3$ is-

  1. $x^2-11x+30=0$
  2. $(x-3)^2-5(x-3)+6=0$
  3. Both $(A)$ and $(B)$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Roots of x^2 - 5x + 6 = 0 are 2 and 3. If roots are A+3 and B+3, they are 5 and 6. The equation is (x-5)(x-6) = x^2 - 11x + 30 = 0. Also, replacing x with x-3 in the original equation gives (x-3)^2 - 5(x-3) + 6 = 0, which is also correct.

AI explanation

Using Vieta's formulas for the equation x^2 - 5x + 6 = 0, the sum of the roots A and B is 5 and their product is 6. For the new roots A+3 and B+3, the sum is (A+B) + 6 = 11, and the product is AB + 3(A+B) + 9 = 6 + 15 + 9 = 30. The required equation is x^2 - 11x + 30 = 0. Alternatively, substituting x-3 for x in the original equation yields (x-3)^2 - 5(x-3) + 6 = 0, which expands to the exact same equation, making both forms correct.

Keep practicing — related questions