(D) For a quadratic polynomial of the form $ax^2 + bx + c$,the sum of the zeros $\alpha + \beta$ is given by the formula $\alpha + \beta = -b/a$.Compa

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(D) For a quadratic polynomial of the form $ax^2 + bx + c$,the sum of the zeros $\alpha + \beta$ is given by the formula $\alpha + \beta = -b/a$.Comparing $p(x) = x^2 - 4x + 3$ with $ax^2 + bx + c$,we get $a = 1$,$b = -4$,and $c = 3$.Substituting these values into the formula: $\alpha + \beta = -(-4)/1 = 4/1 = 4$.Since $4$ is a positive integer,the correct option is $D$.

Class 10 Mathematics Polynomials Relationship between Zeroes and Coefficients of a Polynomial

Medium

For the polynomial $p(x) = x^2 - 4x + 3$,the value of $\alpha + \beta$ is . . . . . . .

A
Zero
B
Negative integer
C
Positive fraction
D
Positive integer

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Class 10

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Chapter

Polynomials

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Relationship between Zeroes and Coefficients of a Polynomial

Prove that $x+2$ is a factor of $p(x)=2x^{3}-4x^{2}+5x+42$.

Medium

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Obtain the quadratic or the cubic polynomial as the case may be in the standard form with the following coefficients: $a=2, b=3, c=-5, d=0$.

Easy

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Find a quadratic polynomial,each with the given numbers as the sum and product of its zeroes respectively: $-\frac{1}{4}, \frac{1}{4}$.

Medium

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Find the division of the following by synthetic division method: $p(x) = x^{3} - 4x^{2} + 5x + 3$ by $x - 2$.

Medium

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Examine the validity of the statement: $(x+3)$ is a factor of $x^{3}+6x^{2}+5x-12$.

Easy

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For the polynomial $p(x) = x^2 - 4x + 3$,the value of $\alpha + \beta$ is . . . . . . .

Similar Questions

Prove that $x+2$ is a factor of $p(x)=2x^{3}-4x^{2}+5x+42$.

Obtain the quadratic or the cubic polynomial as the case may be in the standard form with the following coefficients: $a=2, b=3, c=-5, d=0$.

Find a quadratic polynomial,each with the given numbers as the sum and product of its zeroes respectively: $-\frac{1}{4}, \frac{1}{4}$.

Find the division of the following by synthetic division method: $p(x) = x^{3} - 4x^{2} + 5x + 3$ by $x - 2$.

Examine the validity of the statement: $(x+3)$ is a factor of $x^{3}+6x^{2}+5x-12$.

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