Please solve by factorising
2 answers:
Answer:
x = , x = 5
Step-by-step explanation:
4x² - 23x + 15 = 0
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 4 × 15 = 60 and sum = - 23
The factors are - 20 and - 3
Use these factors to split the x- term
4x² - 20x - 3x + 15 = 0 ( factor the first/second and third/fourth terms )
4x(x - 5) - 3(x - 5) = 0 ← factor out (x - 5) from each term
(x - 5)(4x - 3) = 0
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
4x - 3 = 0 ⇒ 4x = 3 ⇒ x =
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Answer:
<em>18</em> values for n are possible.
Step-by-step explanation:
Given the quadratic polynomial:
such that:
Roots are positive prime integers and
To find:
How many possible values of are there ?
Solution:
First of all, let us have a look at the sum and product of a quadratic equation.
If the quadratic equation is:
and the roots are: and
Then sum of roots,
Product of roots,
Comparing the given equation with standard equation, we get:
A = 1, B = -m and C = n
Sum of roots,
Product of roots,
We are given that
and
are positive prime integers such that their sum is less than 20.
Let us have a look at some of the positive prime integers:
2, 3, 5, 7, 11, 13, 17, 23, 29, .....
Now, we have to choose two such prime integers from above list such that their sum is less than 20 and the roots can be repetitive as well.
So, possible combinations and possible value of are:
So,as shown above <em>18 values for n are possible.</em>