Math, asked by sonukanaujia504, 11 months ago

find the quadratic polynomial whose zeros are 4,1

Answers

Answered by kumarmonu89761
2

Answer:

The required quadratic polynomial whose zeros are 4,1 is x^{2} -5x+4

Step-by-step explanation:

Quadratic polynomial:

When a variable term in the polynomial expression has the highest power of 2, the polynomial is said to be quadratic. Only the exponent of the variable is taken into account when determining a polynomial's degree. It is not taken into account how strong a coefficient or constant term is. A quadratic equation or quadratic function is created when a quadratic polynomial is equal to 0. The roots or zeros of the quadratic equation are the names given to the solutions of such an equation.

Quadratic equation:

x^{2} -(Sum of zeros)x+(product of zeros)

=x^{2} -(4+1)x+(4 * 1)\\=x^{2} -5x+4

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Answered by gayatrikumari99sl
0

Answer:

x^2 - 5x + 4 is the  required quadratic polynomial  whose zeroes are 4 and 1 .

Step-by-step explanation:

Explanation:

Given, a quadratic polynomial whose zeros are 4 and 1 .

As we know, for any polynomial, P(x) = ax^2 + bx + c.

and if \alpha\   and \ \beta be the zeroes of the polynomial then,

Sum of zeroes of a polynomial =  (\alpha  + \alpha)

Product of zeroes polynomial  =   (\alpha \beta)

Step 1:

Given zeroes are 4 and 1

Product of the zeroes = 4 × 1 = 4

 and sum of the zeroes = 4 + 1 = 5

Now, quadratic polynomial can be expressed as ,

x^2 - ( sum of zeroes) x + (product of zeroes)

x^2 - 5x + 4 .

Final answer:

Hence, x^2 - 5x + 4 is the quadratic polynomial whose zeroes are 4 and 1 .

#SPJ1

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