Find the discriminant of this quadratic equation then state the number and type of solution. `-5x^2+x-19= -9`
Given quadratic equation is `-5x^2+x-19=-9` . Which can be written as `-5x^2+x-19+9=0`
The discriminant for the quadratic equation `ax^2+bx+c=0` is defined as `D=b^2-4ac.` Since the given equation is quadratic, it has two solutions described as under-
i) If `D>0` , both roots of the equation are real and distinct.
ii) If `D=0` , both roots of the equation are real and equal.
iii) If `D<0` , both roots of the equation are complex.
Here we see that `a=-5,b=1,c=-10` .
From case (iii) it is clear that roots of given quadratic equation are complex i.e. of the form `a+-ib` .i.e. the first root will be of the form `a+ib` and the second root will be of the form `a-ib.`
The formula of the discriminant of a quadratic equation in a form ax^2+bx+c=0 is b^2-4ac.
Before we apply the formula for the given equation, set one side equal to zero. To do so, add both sides by 9.
Then, plug-in the value of a b and c to the formula of discriminant . The values are a=-5, b=1 and c=-10.
Hence, the discriminant of the given equation is -199.
Since its value is less than zero, the quadratic equation has two complex solutions (non-real numbers).
`5x^2-x+10=0` the a =5 b= -1 c= 10 so:
`Delta= b^2-4ac= (-1)^2- 4( 10)(5)= -199`
since negative, hsn's realsolution but two comple solution.
add the 9 to the other side
`-5x^2+x-19+9=-9+9 ` you will end up with
`a=-5 b=1 c=-10` the formula for finding the discriminant is b^2-4ac plug in the numbers into the formula
`1-200=-199` the discriminant is -399 since it is less than 0 it means there are no real solutions but instead two complex solutions
Given quadratic equation