Meera says: the equation x^2 + 4x + 7 = 0 has no real roots. Using completing the square, x^2 + 4x + 7 = (x + 2)^2 + 3. Why can the equation have no real solution?

Question

Accepted Answer

Because (x + 2)^2 + 3 is always at least 3, never 0. (x + 2)^2 >= 0, so (x + 2)^2 + 3 >= 3 > 0 for all real x. It can never equal 0, hence no real roots.

Meera says: the equation $x^{2} + 4 x + 7 = 0$ has no real roots.
Using completing the square, $x^{2} + 4 x + 7 = (x + 2)^{2} + 3$ .
Why can the equation have no real solution?

Step-by-Step Solution

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More Class 10 Completing the Square practice

Meera says: the equation x2+4x+7=0 has no real roots.Using completing the square, x2+4x+7=(x+2)2+3.Why can the equation have no real solution?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Completing the Square practice

Meera says: the equation $x^{2} + 4 x + 7 = 0$ has no real roots.
Using completing the square, $x^{2} + 4 x + 7 = (x + 2)^{2} + 3$ .
Why can the equation have no real solution?