QUADRATIC EQUATIONS - True/False

Your Progress 0 / 25 attempted
Q 01 / 25
The graph of the quadratic equation \(ax^2 + bx + c = 0\) (where \(a ? 0\)) is always a straight line.
Q 02 / 25
Every quadratic equation has exactly two real roots.
Q 03 / 25
The discriminant of \(x^2 - 4x + 4 = 0\) is zero.
Q 04 / 25
If the roots of \(ax^2 + bx + c = 0\) are real and equal, then \(b^2 - 4ac \gt 0\).
Q 05 / 25
The quadratic formula is \(x =\frac{ -b \pm \sqrt{(b² - 4ac)}} { 2a}\).
Q 06 / 25
For \(2x^2 + 3x - 2 = 0\), the sum of roots is -3/2.
Q 07 / 25
The product of roots of \(x^2 - 5x + 6 = 0\) is 6.
Q 08 / 25
A quadratic equation can have three distinct real roots.
Q 09 / 25
If a and ß are roots of \(x^2 - 7x + 12 = 0\), then a + ß = 7.
Q 10 / 25
The equation \(x^2 = 4\) is a quadratic equation.
Q 11 / 25
For \(x²^2+ 2x + 5 = 0\), the nature of roots is real and distinct.
Q 12 / 25
The roots of \(3x^2 - 6x + 3 = 0\) are real and equal.
Q 13 / 25
If product of roots is negative, both roots have opposite signs.
Q 14 / 25
The equation \((x - 2)(x + 3) = 0\) has roots 2 and -3.
Q 15 / 25
Quadratic equation \(x^2 - 2x - 1 = 0\) has rational roots.
Q 16 / 25
Sum of roots of \(5x^2 - 10x + 7 = 0\) is 2.
Q 17 / 25
If discriminant is positive, roots are always rational.
Q 18 / 25
The quadratic \(x^2 + 4x + 4 = 0\) factors as \((x + 2)^2 = 0\).
Q 19 / 25
For equation \(4x^2 - 12x + 9 = 0\), roots are 3/2, 3/2.
Q 20 / 25
Nature of roots depends only on coefficient a.
Q 21 / 25
Equation \(x^2 - 3x - 10 = 0\) has roots 5 and -2.
Q 22 / 25
If both roots are positive, then a and c have opposite signs.
Q 23 / 25
Discriminant of \(2x^2 + 5x + 3 = 0\) is 1.
Q 24 / 25
Quadratic equation with roots 1, 1 is \(x^2 - 2x + 1 = 0\).
Q 25 / 25
The graph of \(y = -x^2 + 1\) opens upwards.
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