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COMEDK2018MathematicsQuadratic Equation

If a, b, c , and d are the roots of the equation x⁴+2 x³+3 x²+4 x+5=0 , then 1+a²+b²+c²+d² is equal to

Options

  1. A-2
  2. B-1
  3. C2
  4. D1

Correct answer

B. -1

Step-by-step solution

As, gathered (a+b+c+d)²=a²+b²+c²+d² +2(a b+b c+a d+b c+b d+c d) a²+b²+c²+d²=(a+b+c+d)² -2[a b+b c+a c+a d+b d+c d] gathered Now, as a, b, c, d are the roots of the equation. We have, a+b+c+d= -2 1 =-2 and a b+a c+a d+b c+b d+c d= 3 1 =3 We have, 1+a²+b²+c²+d² aligned &=1+(-2)²-2(3) &=1+4-6=-1 aligned

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