$CATEGORY: Maths - TicTacLearn/4. Quadratic equations/4. Quadratic equations--Nature of Roots

//Multiple Choice

The nature of roots of a quadratic equation depends on which of the following? {
~ Sum of the roots
= Discriminant (Δ)
~ Coefficients of the equation
~ Product of the roots
}

If the discriminant (Δ) of a quadratic equation is positive and a perfect square, then the roots are\: {
= Real and unequal
~ Real and equal
~ Imaginary
~ None of these
}

If the quadratic equation \(x^2−6x+9\=0\)  has equal roots, then its discriminant is\: {
= 0
~ 9
~ -9
~ 6
}

The roots of the equation \(3x^2+2x+5\=0\) are\: {
~ Real and equal
~ Real and distinct
= Imaginary
~ None of these
}

If the discriminant (Δ) of a quadratic equation is negative, then the roots are\: {
~ Real and equal
~ Real and distinct
= Imaginary
~ None of these
}

What is the value of the discriminant for the equation \(2x^2−4x+2\=0\)? {
= 0
~ 4
~ -4
~ 2
}

If a quadratic equation has real and equal roots, then the graph of the equation touches the\: {
~ X-axis at two points
= X-axis at one point
~ Y-axis at one point
~ None of these
}

The equation \(x^2+4x+7\=0\) has which type of roots? {
~ Real and unequal
~ Real and equal
= Imaginary
~ None of these
}

//True or False

If the discriminant (Δ) is positive, the roots of the quadratic equation are always equal. {F}

The quadratic equation \(x^2+4x+4\=0\)  has real and equal roots. {T}

If the discriminant is negative, the quadratic equation has two distinct real roots. {F}

The discriminant of \(x^2−4x+4\=0\) is 0. {T}

A quadratic equation always has two roots, whether real or complex. {T}

//Numericals



//Fill in the blanks

The roots of a quadratic equation depend on the value of the _________. {
~ coefficient of x
= discriminant
~ sum of roots
~ none
}

If Δ>0 , the roots are _________. {
~ real and equal
= real and distinct
~ imaginary
~ none
}

If Δ\=0 , the roots are _________. {
= real and equal
~ real and distinct
~ imaginary
~ none
}

If the discriminant of a quadratic equation is negative, the roots are _________. {
~ real and equal
~ real and distinct
= imaginary
~ none
}

The discriminant of \(x^2+2x+1\=0\) is _________. {
= 0
~ 1
~ -1
~ 2
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=\(x^2−6x+9\=0\) -> Real and equal roots
=\(x^2−4x−5\=0\) -> Real and distinct roots
=\(x^2+3x+2\=0\) -> Real and unequal roots
=\(x^2+x+1\=0\) -> Imaginary roots
}



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