Class 10 Quiz Level 3 (Difficult) – Quadratic Equations

Total questions: 10

If the quadratic equation $ \displaystyle 3{{x}^{2}}-2kx+4=0$ has no real roots, what can be said about $ \displaystyle k$?

Topic: Nature of Roots

Deselect Answer

$ \displaystyle \left| k \right|>2\sqrt{3}$

$ \displaystyle \left| k \right|<2\sqrt{3}$

$ \displaystyle \left| k \right|=2\sqrt{3}$

$ \displaystyle \left| k \right|=0$

None

For which of the following values of $ \displaystyle m$ will the quadratic equation $ \displaystyle {{x}^{2}}+2mx+\left( {{{m}^{2}}-m} \right)=0$ have equal roots?

Topic: Discriminant and Nature of Roots

Deselect Answer

$ \displaystyle m=0$

$ \displaystyle m=1$

$ \displaystyle m=2$

$ \displaystyle m=\dfrac{1}{2}$

None

Solve the quadratic equation $ \displaystyle 4{{x}^{2}}+5x-1=0$ using the quadratic formula. What are the roots?

Topic: Quadratic Formula Application

Deselect Answer

$ \displaystyle x=\dfrac{{-5\pm \sqrt{{41}}}}{8}$

$ \displaystyle x=\dfrac{{-5\pm \sqrt{{21}}}}{8}$

$ \displaystyle x=\dfrac{{5\pm \sqrt{{41}}}}{8}$

$ \displaystyle x=\dfrac{{5\pm \sqrt{{21}}}}{8}$

None

Find the maximum value of the quadratic function $ \displaystyle y=-3{{x}^{2}}+6x+4.$

Topic: Maximum or Minimum Value

Deselect Answer

None

The quadratic equation $ \displaystyle {{x}^{2}}+px+q=0$ has complex roots. What must be true about the discriminant?

Topic: Nature of Roots

Deselect Answer

Discriminant is positive

Discriminant is negative

Discriminant is zero

Discriminant is non-negative

None

Find the maximum value of the quadratic function $ \displaystyle y=-3{{x}^{2}}+12x-7.$

Topic: Maximum and Minimum Value

Deselect Answer

None

The vertex of the parabola $ \displaystyle y=3{{x}^{2}}-18x+27$ lies on which line?

Topic: Vertex of a Parabola

Deselect Answer

$ \displaystyle y=-9$

$ \displaystyle x=3$

$ \displaystyle y=9$

$ \displaystyle x=-3$

None

Determine the minimum value of the quadratic function $ \displaystyle y=2{{x}^{2}}-8x+7$.

Topic: Maximum and Minimum Value

Deselect Answer

-1

None

Solve the quadratic equation $ \displaystyle 3{{x}^{2}}+2x-1=0$ using the quadratic formula. What are the roots?

Topic: Quadratic Formula Application

Deselect Answer

$ \displaystyle x=\dfrac{{-2\pm \sqrt{{16}}}}{6}$

$ \displaystyle x=\dfrac{{-2\pm \sqrt{8}}}{6}$

$ \displaystyle x=\dfrac{{2\pm \sqrt{8}}}{6}$

$ \displaystyle x=\dfrac{{2\pm \sqrt{{16}}}}{6}$

None

10.

For what value of $ \displaystyle m$ does the quadratic equation $ \displaystyle {{m}^{2}}{{x}^{2}}+\left( {m+1} \right)x+1=0$ have real roots?

Topic: Discriminant and Nature of Roots

Deselect Answer

$ \displaystyle m\ge -2$

$ \displaystyle m>0$

$ \displaystyle m<0$

$ \displaystyle m\le -2$

None

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Class 10 Quiz Level 3 (Difficult) – Quadratic Equations

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