$CATEGORY: Maths - TicTacLearn/2. Polynomials/2. Polynomials--Relationship between Zeroes and Coefficients of a Polynomial

//Multiple Choice

If α and β are the zeroes of the quadratic polynomial , \(ax^2+bx+c\) what is the sum of the zeroes? {
= -b/a
~ b/a
~ -c/a
~ c/a
}

What is the product of zeroes of the quadratic polynomial \(ax^2+bx+c\) {
~ -b/a
= c/a
~ -c/a
~ b/a
}

The quadratic polynomial with zeroes 3 and -4 is {
~ \(x^2-x+12\)
~ \(x^2+x-12\)
= \(x^2-x-12\) 
~ \(x^2+x+12\)
}

If the zeroes of a polynomial are equal, then the discriminant is {
~ Positive
~ Negative
= Zero
~ Undefined
}

For the cubic polynomial \(ax^3+bx^2+cx+d\), the sum of the zeroes is {
= -b/a
~ c/a
~ -c/a
~ b/a
}

For the cubic polynomial \(ax^3++bx^2+cx+d\), the product of the zeroes is {
= -d/a
~ d/a
~ -b/a
~ c/a
}

If one of zeroes of \(2x^2+7x+k\) is 3 then the value of k is {
= -27
~ 27
~ -21
~ 21
}

If zeroes of a quadratic polynomial are 5 and -2 the polynomial is {
~ \(x^2-3x-10\)
= \(x^2+3x-10\)
~ \(x^2-3x+10\)
~ \(x^2+3x+10\)
}

The sum and product of the zeroes of a polynomial \(x^2-4x+4\) are {
= 4 and 4
~ -4 and 4
~ 4 and -4
~ -4 and -4
}

If the zeroes of a polynomial x^2+px+q are reciprocal to each other then {
~ p\=q
~ p\=0
= q\=1
~ p\=1
}

//True or False

The sum of the zeroes of the quadratic polynomial is \(ax^2+bx+c\) is -b/a . {T}

The product of the zeroes of the quadratic polynomial  is \(ax^2+bx+c\) is -c/a {F}

If the zeroes of a polynomial are equal, the discriminant is zero. {T}

The quadratic polynomial \(x^2-4x+4\) has zeroes 2 and -2. {F}

For the cubic polynomial \(ax^3+bx^2+cx+d\), the product of the zeroes is  -d/a . {T}

If one of the zeroes of the polynomial \(2x^2+7x+k\) is 3, the value of  is -27. {T}

The sum of the zeroes of the polynomial  \(x^2+px+q\) is always equal to p. {F}

If the zeroes of a polynomial are reciprocal to each other, the constant term is 1. {T}

The quadratic polynomial with zeroes 4 and -5 is \(x^2-x-20\). {T}

The relationship between zeroes and coefficients is valid only for quadratic polynomials. {F}


//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=\(x^2-5x+6\) -> zeroes are 2 and 3
=\(x^2+3x+2\) -> sum of zeroes \=-3
=\(x^2-4x+4\) -> product of zeroes\=4
=\(x^2+2x+1\) -> both zeroes are equal
}



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