In the denominator, 2(3) does not equal 4.lloydowen said:[itex] 3t^2+7t-5=0
t= \frac{-7 +or-\sqrt{7^2-4(3)(-5)}}{2(3)}
t= \frac{-7+\sqrt{109}}{4}
t= -4.39
[/itex] OR...
[itex]t= \frac{-7-\sqrt{109}}{4}
t= -9.61 [/itex]
The reason I have doubts is because the answer book from the tutor shows, T= 0.573 or -2.907... ? :(
A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and x is the variable. It is a polynomial equation of degree 2 and has the general solution of x = (-b ± √(b^2 - 4ac)) / 2a.
To solve a quadratic equation, you can use the quadratic formula or factorization. To use the quadratic formula, substitute the values of a, b, and c into the formula and solve for x. To factorize, find two numbers that multiply to give ac and add to give b. Then, rewrite the equation as (ax + m)(ax + n) = 0 and solve for x.
The discriminant is the part of the quadratic formula under the square root sign, b^2 - 4ac. It is used to determine the nature of the roots of a quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If it is zero, the equation has one real root. And if it is negative, the equation has two complex roots.
Yes, as a scientist, I can check your workings for a quadratic equation. It is important to show all your steps and use correct mathematical notation. I can also provide feedback and suggest alternative approaches if needed.
Some common mistakes when solving quadratic equations include forgetting to include the ± sign in the quadratic formula, misinterpreting the signs of the constants a, b, and c, and making calculation errors. It is also important to check if the final solutions make sense in the context of the original problem.