Question
Question: How do you solve \[2{{x}^{2}}-9x+7=0\]?...
How do you solve 2x2−9x+7=0?
Solution
Use the middle term split method to factorize 2x2−9x+7 and write it as a product of two terms given as (x−a)(x−b) where ‘a’ and ‘b’ are called zeroes of the polynomial. Now, substitute each term equal to 0 and find the two values of x to get the answer.
Complete step-by-step solution:
Here, we have been provided with the quadratic equation 2x2−9x+7=0 and we are asked to solve it. That means we have to find the values of x.
Now, let us apply the middle term split method to factorize the given equation first. Let us assume 2x2−9x+7=f(x), so we have,
⇒f(x)=2x2−9x+7
According to the middle term split method we have to break -9x into two terms such that their sum is -9x and product is equal to the product of constant term (7) and 2x2, i.e., 14x2. So, breaking -9x into -7x and -2x, we get,
(i) (−7x)+(−2x)=−9x
(ii) (−7x)×(−2x)=14x2
Therefore, both the conditions of the middle term split method are satisfied, so we can write the given expression as: -