Question

Find the sum and product of the roots of the quadratic equation 2x²-9x+4=0

Answer 1

Sum of the roots = 9/2

Product of the roots = 2

Explanation:

Step 1: Determine the roots of the quadratic equation:

General equation of the standard form:

The equation 2x²-9x+4 = 0 is in the standard form of a quadratic equation, whose general equation is given by:

`ax^2+bx+c=0`, where:

• a, b, and c are constants.

Finding the roots using the quadratic equation:

We can find the roots of the quadratic equation using the quadratic formula, which is given by:

`x=(-b+/-√(b^2-4ac) )/(2a)`, where:

• a, b, and c are the same constants from the standard form,
• and x is (or are) the root(s).

Thus, we can find the root(s) by substituting 2 for a, -9 for b, and 4 for c in the quadratic equation:

`x=(-(-9)+/-√((-9)^2-4(2)(4)) )/(2(2))\\ \\x=(9+/-√(49) )/(4)`

Now we can begin splitting the answer since a quadratic function can have both both a positive and negative (this is because squaring both a positive and negative number yields a positive number as 2^2 = 4 and (-2)^2 = 4).:

Positive root:

`x=(9)/(4)+(7)/(4),\\ \\ x=16/4\\\\x=4`

Thus, one of the roots is 4.

Negative root:

`x=(9)/(4)-(7)/(4)\\ \\ x=(2)/(4)\\ \\x=(1)/(2)`

Thus, the smaller root is 1/2.

Step 2: Find the sum of 4 and 1/2:

Sum = 4 + 1/2

Sum = 4 1/2

Sum = 9/2

Thus, the sum of 4 and 1/2 is 9/2.

Step 3: Find the product of 4 and 1/2:

Product = 4 * 1/2

Product = 4/2

Product = 2

Thus, the product of 4 and 1/2 is 2.