Question

Question 20 of 25
1 Point
After being rearranged and simplified, which equation cannot be solved using
the quadratic formula?
O
O
A. x2 - 6x- 7 = 2x
B. 2x2 – 3x+ 10 = 2x2 + 21
O
C. 5x2 – 3x + 10 = 2x2
O D. 2x - 4 = 2x2

Answer 1

Answer:

B. $2x^{2}-3x+10=2x^{2}+21$

Step-by-step explanation:

A quadratic equation is of the form $ax^{2} +bx +c=0$, where, a,b and c are any real numbers and $a\ne 0$.

The quadratic formula is given as:

$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

Here, the value of $a$ can't be 0.

Now, the necessary condition to check if quadratic formula can be used in the given equations is to check the value of $a$ after rearranging them in the standard form.

Let us check each expression for the value of $a$.

Option A:

$x^{2}-6x-7=2x\\x^{2}-6x-2x-7=0\\x^{2}-8x-7=0$

Here, $a=1$. So, we can use quadratic formula.

Option B:

$2x^{2}-3x+10=2x^{2}+21\\ 2x^{2}-2^{2}-3x+10-21=0\\0x^{2}-3x-11=0$

Here, $a=0$. So, we can't use quadratic formula.

Option C:

$5x^{2}-3x+10=2x^{2}\\5x^{2}-2x^{2}-3x+10=0\\3x^{2}-3x+10=0$

Here, $a=3$. So, we can use quadratic formula.

Option D:

$2x-4=2x^{2}\\-2x^{2}+2x-4=0$

Here, $a=-2$. So, we can use quadratic formula.

So, only option B has $a=0$. So, we can't use quadratic formula for option B.