$CATEGORY: Maths - TicTacLearn/2. Polynomials/2. Polynomials--Geometrical Meaning of the Zeroes of a polynomial

//Multiple Choice

The maximum number of zeroes , a quadratic polynomial can have is {
~ 1
= 2
~ 3
~ 4
}

The number of zeroes of a quadratic polynomial is equal to the number of points where it's graph {
~ Touches of y-axis
= Intersects the x-axis
~ Lies above the x-axis
~ Lies below the x-axis
}

If the graph of y\=p(x) Touches the x-axis at one point, the quadratic polynomial has {
~ no zeroes
= one zero
~ two zeroes
~ infinite zeroes
}

If the discriminant \(b^2-4ac\) of  p(x)\=\(ax^2+bx+c\) is positive, then the number of zeros is {
~ 0
~ 1
= 2
~ Cannot be determined
}

If the graph y\=p(x) does not intersect the x-axis, the quadratic polynomial has {
= no real zeroes
~ one real zero
~ two real zeroes
~ Infinite real zeroes
}

If y\=\(ax^2+bx+c\), if a>0 and \(b^2-4ac<0\), the number of real zeroes is {
= 0
~ 1
~ 2
~ Cannot be determined
}

The number of zeroes of y\=p(x) can be determined by analysing the {
~ Coefficient of x^2
~ Constant term
= Discriminant
~ Degree of a polynomial
}

If y\=p(x) interests the x-axis at exactly two points, the number of zeroes is {
~ 0
~ 1
= 2
~ Cannot be determined
}

If y\=p(x), if \(b^2-4ac\=0\), the number of zeroes is {
~ 0
= 1
~ 2
~ Infinite
}

If the graph y\=p(x) Lies entirely above the x-axis, the number of real zeroes is {
= 0
~ 1
~ 2
~ Cannot be determined
}

//True or False

If a<0 and \(b^2-4ac<0\) the graph of y\=p(x) lies entirely below the x-axis {T}

A quadratic polynomial with two distinct real roots has a discriminant greater than zero. {T}

If the graph y\=p(x) interests the x- axis at two points, the polynomial has exactly one real root. {F}

A quadratic polynomial with \(b^2-4ac\=0\) has two real roots. {F}

The graph of y\=p(x) always passes through the y- axis.  {T}

If c\=0 in \(y\=ax^2+bx+c\), then the graph of the polynomial passes through the origin. {T}

A quadratic polynomial with \(b^2-4ac>0\) has no real zeroes. {F}

The sum of zeroes of a quadratic polynomial ax^2+bx+c is always equal to -b/a {T}

If y\=p(x) has no real zeroes, the graph does not intersect the x- axis. {T}

The number of zeroes of y\=p(x) can be determined by the graph even without calculating the discriminant. {T}

//Numericals



//Fill in the blanks



//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=Discriminant >0 -> two distinct real zeroes
=Discriminant \=0 -> one real and one equal to zero
=Discriminant <0 -> no real zero
=Graph Intersects the x- axis at one point -> Touches the x - axis
}



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