Find the zeros of the following Quadratic polynomials and verify the relation between the zeros and coefficient.
(i) 3x²-x-4
Answers
QUESTION : Find the zeros of the following Quadratic polynomials and verify the relation between the zeros and coefficient.
(i) 3x²-x-4
ANSWER : the zeros of the following Quadratic polynomials and verify the relation between the zeros and coefficient.
the zeros of the following Quadratic polynomials and verify the relation between the zeros and coefficient. (i) 3x²-x-4
answer - 3x2−x−4=(3x−4)(x+1).
STEP BY STEP EXPLANATION: In the given polynomial 3x2−x−4,
In the given polynomial 3x2−x−4,The first term is 3x2 and its coefficient is 3.
In the given polynomial 3x2−x−4,The first term is 3x2 and its coefficient is 3.The middle term is −x and its coefficient is −1.
In the given polynomial 3x2−x−4,The first term is 3x2 and its coefficient is 3.The middle term is −x and its coefficient is −1.The last term is a constant term −4.
In the given polynomial 3x2−x−4,The first term is 3x2 and its coefficient is 3.The middle term is −x and its coefficient is −1.The last term is a constant term −4.Multiply the coefficient of the first term by the constant 3×−4=−12.
In the given polynomial 3x2−x−4,The first term is 3x2 and its coefficient is 3.The middle term is −x and its coefficient is −1.The last term is a constant term −4.Multiply the coefficient of the first term by the constant 3×−4=−12.We now find the factor of −12 whose sum equals the coefficient of the middle term, which is −1 and then factorize the polynomial 3x2−x−4 as shown below:
In the given polynomial 3x2−x−4,The first term is 3x2 and its coefficient is 3.The middle term is −x and its coefficient is −1.The last term is a constant term −4.Multiply the coefficient of the first term by the constant 3×−4=−12.We now find the factor of −12 whose sum equals the coefficient of the middle term, which is −1 and then factorize the polynomial 3x2−x−4 as shown below:
In the given polynomial 3x2−x−4,The first term is 3x2 and its coefficient is 3.The middle term is −x and its coefficient is −1.The last term is a constant term −4.Multiply the coefficient of the first term by the constant 3×−4=−12.We now find the factor of −12 whose sum equals the coefficient of the middle term, which is −1 and then factorize the polynomial 3x2−x−4 as shown below: 3x2−x−4=3x2+3x−4x−4=3x(x+1)−4(x+1)=(3x−4)(x+1)
In the given polynomial 3x2−x−4,The first term is 3x2 and its coefficient is 3.The middle term is −x and its coefficient is −1.The last term is a constant term −4.Multiply the coefficient of the first term by the constant 3×−4=−12.We now find the factor of −12 whose sum equals the coefficient of the middle term, which is −1 and then factorize the polynomial 3x2−x−4 as shown below: 3x2−x−4=3x2+3x−4x−4=3x(x+1)−4(x+1)=(3x−4)(x+1)Hence, 3x2−x−4=(3x−4)(x+1).
3x²-x-4=0 Product: -12, Sum: -1, Numbers: 3, -4
3x²+3x-4x-4=0
3x(x+1)-4(x+1)= 0
(3x-4) (x+1)=0
x=4/3 x= -1
Sum of zeros
=4/3-1
= (4-3)/1
=1/3
= -(coefficient of x)/coefficient of x ²
Product of zeros
= 4/3* -1
=-4/3
= constant term/ coefficient of x²
Hence verified
Hope it helps:)