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For the following quadratic equation, find the discriminant.

-9x^(2)-70 x-245=-4x^(2)
Answer:

For the following quadratic equation, find the discriminant.\newline9x270x245=4x2 -9 x^{2}-70 x-245=-4 x^{2} \newlineAnswer:

Full solution

Q. For the following quadratic equation, find the discriminant.\newline9x270x245=4x2 -9 x^{2}-70 x-245=-4 x^{2} \newlineAnswer:
  1. Simplify Quadratic Equation: First, we need to simplify the quadratic equation by moving all terms to one side to get it into standard form ax2+bx+c=0ax^2 + bx + c = 0.
    9x270x245=4x2-9x^2 - 70x - 245 = -4x^2
    Add 4x24x^2 to both sides to combine like terms.
    (9x2+4x2)70x245=0(-9x^2 + 4x^2) - 70x - 245 = 0
    5x270x245=0-5x^2 - 70x - 245 = 0
  2. Find Discriminant: Now that we have the quadratic equation in standard form, we can find the discriminant. The discriminant of a quadratic equation ax2+bx+cax^2 + bx + c is given by b24acb^2 - 4ac. For our equation, a=5a = -5, b=70b = -70, and c=245c = -245.
  3. Calculate Discriminant: Calculate the discriminant using the values of aa, bb, and cc.
    Discriminant = b24acb^2 - 4ac
    Discriminant = (70)24(5)(245)(-70)^2 - 4(-5)(-245)
  4. Perform Calculations: Perform the calculations.\newlineDiscriminant = 49004(5)(245)4900 - 4(-5)(-245)\newlineDiscriminant = 490049004900 - 4900
  5. Final Result: After calculating, we find that the discriminant is 00. \newlineDiscriminant = 00

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