Question

2. Ravi claims that the polynomial p(x) = mxa + x26+ has 4b zeroes. For Ravi's
claim to be correct, which of these must be true?
a: a = 2b or a = 4b
b: a = 2 or a = 4b
C: m = 25
d: m = 4b​

Answer 1

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If α and β are zeroes of the polynomial p(x)=2x

2

−7x+3, find the value α

Answer

Correct option is

C

4

37

Given that,

α,β are the zeroes of the polynomial p(x)=2x

2

−7x+3

Sum of zeroes (α+β)=

a

−b

=

2

−(−7)

=

2

7

Product of zeroes αb=

a

c

= −2(

2

3

Let a,b,c be real such that ax

2

+bx+c=0 and x

2

+x+1=0 have a common root.

STATEMENT-1 : a=b=c

Reason

STATEMENT-2: Two quadratic equations with real coefficients cannot have only one imaginary common root.

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View solution

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The roots of the equation x

2

−3x+b=0 differ by 4, then show that 9a

2

=4b+16

Answer 2

The correct option is (a) a = 2b or a = 4b.

Degree of polynomial:

The degree of a polynomial is the biggest or highest power of a variable in a polynomial equation.

Zeroes of polynomial:

All the x-values that make the polynomial equal to 0 are called the zeros of a polynomial p(x).

Explanation:

$mx^{a} +x^{2b}$ has $4b$ zeroes means that this polynomial have number of zeroes is equal to  $4b$ .

The degree of a polynomial is equal to the number of zeroes in that polynomial, as we know. And degree (maximum power of variable or x) is an in this case.

So, degree of polynomial = number of zeroes of the polynomial

Degree of polynomial is a and 2b.

Zeros of polynomial is 4b.

Equating both, we get

So, a = 4b and a = 2b

Thus, the given polynomial had a values, a = 4b and a = 2b.

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