Question

under what condition will ax^2 + 5x+7=0 be a quadratic equation?

Answer 1

Answer:

The solution to the equation is composed of roots x=−5+√3i2 and x=−5−√3i2.

Explanation:

Based on the quadratic formula x=−b±√b2−4ac2a and the form ax2+bx+c=0, we see that a=1, b=5 and c=7.

By substitution, x=−5±√52−4⋅1⋅72⋅1

x=−5±√25−282
x=−5±√−32

With i=√−1, x=−5±√3i2.

Thus, the roots of the equation are x=−5+√3i2 and x=−5−√3i2.

Answer 2

The condition that ax² + 5x + 7 = 0 will be a quadratic equation is a ≠ 0

Given :

The equation ax² + 5x + 7 = 0

To find :

The condition that ax² + 5x + 7 = 0 will be a quadratic equation

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation is

ax² + 5x + 7 = 0

Step 2 of 2 :

Find the required condition

We know that for a quadratic equation the highest power of its variable that appears with nonzero coefficient is 2

For the equation ax² + 5x + 7 = 0 the variable is x

Now the equation ax² + 5x + 7 = 0 will be a quadratic equation if

Coefficient of x² ≠ 0

⇒ a ≠ 0

Hence the condition that ax² + 5x + 7 = 0 will be a quadratic equation is a ≠ 0

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