Question

Ravi claims that the polynomial p(x) = mx^a + x^2b has 4b zeroes. For Ravi's claim to be correct, which of these must be true?​
Option 1: a= 2b or a = 4b
Option 2: a = 2 or a = 4b
Option 3: m = 2b
Option 4: m = 4b

Answer 1

we have given that,

Ravi claims that the polynomial p(x) = mx^a + x^2b has 4b zeroes. For Ravi's claim to be correct

Find:

which of these options must be true.

“(A) a= 2 or a = 4″ has been changed to “(A) a= 2b or a = 4b”

Hence, the option 1 is correct.

Answer 2

Answer:

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

As we know the degree of the polynomial is equal to number of zeroes of that polynomial. And here degree( highest power of variable or x) is a.

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

So, a = 4b

for example

if we take a quadratic polynomial that is 3x^2+4x+5 then degree of polynomial is 2 hence number of zeroes of this polynomial is 2.

Same as for cubic polynomial if we take a cubic polynomial that is 3x^3+6x^2+3x+9 then the degree if polynomial is 3 and hence number of zeroes of the polynomial is also 3.

option 1 a = 2b a = 4b