Multiple choice

Sum and product of the roots of the quadratic equation $\displaystyle { 2x }^{ 2 }-3x+4=0$ are :

  1. $\displaystyle -\frac { 7 }{ 2 } ,2$
  2. $\displaystyle \frac { 7 }{ 2 } ,\frac { 3 }{ 2 } $
  3. $\displaystyle \frac { 5 }{ 2 } ,\frac { 3 }{ 2 } $
  4. $\displaystyle \frac { 3 }{ 2 } ,2$
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D Correct answer
Explanation

For ax^2 + bx + c = 0, sum of roots = -b/a and product = c/a. Here, a=2, b=-3, c=4. Sum = -(-3)/2 = 3/2. Product = 4/2 = 2.

AI explanation

The sum and product of the roots of a quadratic equation ax^2 + bx + c = 0 are given by the formulas -b/a and c/a respectively. For the equation 2x^2 - 3x + 4 = 0, the coefficients are a = 2, b = -3, and c = 4. Applying the formulas, the sum is -(-3)/2 = 3/2 and the product is 4/2 = 2.

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