Find the Zeros of the Quadratic Polynomial x² + 7x + 12 and Verify the Relationship Between the Zeros and the Coefficients

Find the Zeros of the Quadratic Polynomial x² + 7x + 12 and Verify the Relationship Between the Zeros and the Coefficients

Solution:

To find the zeros of the quadratic polynomial x²+7x+12, we need to factorize the polynomial or use the quadratic formula.

Let’s factorize it:

x²+7x+12=(x+3)(x+4)

Setting each factor equal to zero, we get:

x+3 = 0 and x+4 = 0

Solving for x in each equation, we find: x=-3 and x=-4

Therefore, the zeros of the quadratic polynomial x²+7x+12 are -3 and -4. Now, let’s verify the relationship between the zeros and the coefficients. For a quadratic polynomial of the form ax²+bx+c, the relationship between the zeros (x₁ and x₂) and the coefficients is given by Vieta’s formulas:

Sum of the zeros: x₁+x₂=-b/a

Product of the zeros: x₁.x₂=c/a

In this case, a=1, b=7, c=12, x₁=-3, and x₂=-4

Sum of the zeros: (-3)+(-4) = -7 = -7/1 = -b/a

Product of the zeros: (-3)⋅(-4) = 12 = 12/1 = c/a

Both relationships hold true, verifying the relationship between the zeros and the coefficients of the quadratic polynomial x²+7x+12.

Answer:

The Zeros of the Quadratic Polynomial x² + 7x + 12 are x=-3 and x=-4 and Verifies the Relationship Between the Zeros and the Coefficients.

Similar Questions:

• What Should be Added to the Quadratic Polynomial x²-5x+4 so that 3 is a Zero of the Resulting Polynomial?
• If one Zero of Polynomial (a^2 + 9) x^2 + 13x + 6a is Reciprocal of other, Find Value of a
• If the Squared Difference of the Zeros of Polynomial x2+px+45 is 144 Then Find p
• Find the Zeros of the Following Quadratic Polynomials x²+7x+10 and Verify the Relationship between the Zeros and the Coefficients
• If sum of the zeroe of the polynomial Ky^2+2y-3K is twice their product of zeros then find the value of K
• If α and β are Zeros of Polynomial x²+6x+9, then Form a Quadratic Polynomial whose Zeros are -alpha, -beta.
• On Solving Each of the Following Quadratic Equations: a/(x-b)+b/(x-a)=2, we get x=(a+b/2) and x=(a+b)