Question

Determine the type and number of solutions of -4x^2-3x+7=0

Answer 1

Quadratic equation and two distinct real solutions

Explanation:

Given equation is

-4x²-3x+7 = 0

We have to determine the type of equation and number of solution.

For type of equation,

Highest power of equation is 2.

Hence, equation is quadratic equation.

Now,For number of solution:

ax²+bx+c = 0 is general quadratic equation.

Comparing general equation with given equation, we have

a = -4, b = -3 and c = 7

We use the formula of discriminant.

D = b²-4ac

D = (-3)²-4(-4)(7)

D = 9+112

D = 121 > 0

Hence, Discriminant is real.

Hence, there are two distinct real solutions of given equation.

Answer 2

`x_(1)=1 \ and \ x_(2)=-(7)/(4)`

Explanation:

The equation:

`-4x^2-3x+7=0`

Can be solved by using the quadratic formula:

`x=(-b\pm√(b^2-4ac))/(2a) \\ \\ where \\ a=-4 \\ b=-3 \\ c=7 \\ \\ x=(-(-3)\pm√((-3)^2-4(-4)(7)))/(2(-4)) \\ \\ x=(3\pm√(9+112))/(-8) \\ \\ where: \\ \\ x_(1)=1 \ and \ x_(2)=-(7)/(4)`

These two values represents the zeroes of the polynomial function
`f(x)=-4x^2-3x+7`