# Which of the following equations has real solutions: 3x^2 - 8x + 4 = 0 2x^2 + x - 1 = 0 x^2 + 9 = 0 5x^2 + 2x - 6 = 0

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### 1 Answer

A quadratic equation ax^2 + bx + c = 0 has real solutions if the value of b^2 - 4*a*c is greater than or equal to 0. For the equations given:

3x^2 - 8x + 4 = 0 : b^2 - 4ac = 64 - 4*3*4 = 16

This equation has real roots.

2x^2 + x - 1 = 0 : b^2 - 4ac = 1 + 1*2*4 = 9

This equation also has real roots

x^2 + 9 = 0 : b^2 - 4ac = 0 - 36 = -36

This equation has complex roots

5x^2 + 2x - 6 = 0 : b^2 - 4ac = 4 + 4*5*6 = 124

This equation has real roots.

**Of the equations given those that have real roots are 3x^2 - 8x + 4 = 0, 2x^2 + x - 1 = 0 and 5x^2 + 2x - 6 = 0**